User:Nomalias

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blablabla

start-93(11/10/2020)

polynomials

Chebotarev theorem on roots of_unity generating question 1gq 2gq3gq4

fourier vs contour

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terms

https://en.wikipedia.org/wiki/Arithmetic_geometry https://en.wikipedia.org/wiki/Arithmetic_dynamics https://en.wikipedia.org/wiki/Arithmetic_topology
https://en.wikipedia.org/wiki/Topological_graph_theory https://en.wikipedia.org/wiki/Shape_theory_(mathematics)

weird

Replica trick++++

snippets

Hilbert 10th problem Pell's conics elliptic curves parallel

Countable state space Continuous or general state space
Discrete-time (discrete-time) Markov chain on a countable or finite state space Harris chain (Markov chain on a general state space)
Continuous-time Continuous-time Markov process or Markov jump process Any continuous stochastic process with the Markov property, e.g., the Wiener process

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Diophantine equations Dynamical systems
Rational and integer points on a variety Rational and integer points in an orbit
Points of finite order on an abelian variety Preperiodic points of a rational function

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https://en.wikipedia.org/wiki/Template:Commutative_local_ring_classes https://en.wikipedia.org/wiki/Template:Commutative_ring_classes https://en.wikipedia.org/wiki/Template:Algebraic_structures https://en.wikipedia.org/wiki/Template:Analogous_fixed-point_theorems


https://en.wikipedia.org/wiki/Category:Mathematics_navigational_boxes


stack stuff

+ + toric=>rational+ +

stack stuff 2

[1]

stuff

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https://en.wikipedia.org/wiki/Zsigmondy's_theorem



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Hausdorff moment problem Stieljes moment problem Hamburger moment problem


https://en.wikipedia.org/wiki/Highly_composite_number https://en.wikipedia.org/wiki/Van_Eck's_sequence


https://en.wikipedia.org/wiki/Dirichlet_kernel https://en.wikipedia.org/wiki/Weyl_character_formula#The_SU(2)_case https://en.wikipedia.org/wiki/Chern-Simons_theory#HOMFLY_and_Jones_polynomials


https://en.wikipedia.org/wiki/Frobenius_reciprocity


https://en.wikipedia.org/wiki/Cyclotomic_polynomial https://proofwiki.org/wiki/Reciprocals_of_Odd_Numbers_adding_to_1


https://en.wikipedia.org/wiki/Chebyshev_function#The_Riemann_hypothesis https://en.wikipedia.org/wiki/Explicit_formulae_(L-function)#Weil's_Explicit_Formula https://en.wikipedia.org/wiki/Hilbert–Pólya_conjecture https://mathoverflow.net/questions/62816/the-guinand-weil-explicit-formula-without-entire-function-theory?rq=1


https://en.wikipedia.org/wiki/Cassini_and_Catalan_identities


https://en.wikipedia.org/wiki/Generating_function



combinatorics

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Universality stuff

https://en.wikipedia.org/wiki/Feigenbaum_constants https://en.wikipedia.org/wiki/Misiurewicz_point https://en.wikipedia.org/wiki/Albert_J._Libchaber#Research https://en.wikipedia.org/wiki/Sharkovskii's_theorem https://en.wikipedia.org/wiki/Kondo_effect https://en.wikipedia.org/wiki/Beta_function_(physics) https://en.wikipedia.org/wiki/Critical_exponent https://en.wikipedia.org/wiki/Universality_class https://en.wikipedia.org/wiki/Kibble-Zurek_mechanism


https://en.wikipedia.org/wiki/Foias_constant


Correspondences&dictionaries

https://ncatlab.org/nlab/search?query=correspondence + Schreiber's correspondences+


Correspondences:
algebraic sets & Ideals
Field subextension & Galois Subgroups
Galois group & Fundemantal group + + +
algebra/geometry & galois/fundamental group Modular forms & Elliptic curves
Automorphic forms & Algebraic curves
Elliptic modular forms & Group representations

Geometric langlands
Kobayashi–Hitchin correspondence
Simpson correspondence
Riemann-Hilbert correspondence
Robinson-Schensted correspondence
Shimura correspondence-Theta correspondence


Haussdorf-C* algebra duality + + + Lawrence theory Morita's equivalence


homology-homotopy dictionary+
number field-function field dictionary
Kapranov-Reznikov-Mazur dictionary/arithmetic topology + + + + + arithmetic/knots dictionary +
Diophantine dictionary/Arithmetic dynamics
algebraic geometry dictionary +
wu-yang dictionary
eigensheaf-eigenbrane relation elliptic-parabolic dictionary feynman-intersection number dictionary-like GKPW dictionary+


votja's conjecture+


Baez-Stay dictionary


https://en.wikipedia.org/wiki/Category:Duality_theories


https://en.wikipedia.org/wiki/Lie_group-Lie_algebra_correspondence#Proof_of_the_homomorphisms_theorem


Generalizations


(Milnor conjecture-Thom conjecture) (Witten conjecture-Virasoro conjecture) (K theory-L theory) (Pontryagin_duality-Tannaka-Krein duality+) (Maximun principle-Hopf's Maximum principle) (Padé series-Laurent series-Puiseux series) (Weierstrass factorization-Mittag-Leffer's factorization) (Stone-Weierstrass theorem-Arakelyan's_theorem) (Cantor's_paradox-Ordinal Cantor's paradox(+)) (Russell's_paradox-Girard's_paradox) (Stone's theorem-Stone-von Neumann theorem) (Morse theory-Picard-Lefschetz theory) (Invariant theory-Geometric invariant theory) (https://en.wikipedia.org/wiki/Differential_Galois_theory) (Borel–Weil–Bott theorem-GAGA) (Kloosterman sum-Ramanujan sum) (Weierstrass preparation theoremMalgrange preparation theorem)


classification miscelanea


https://en.wikipedia.org/wiki/Uniqueness_theorem


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Invariant miscelanea

(Invariant theory-Geometric invariant theory)


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https://en.wikipedia.org/wiki/Invariant_differential_operator https://en.wikipedia.org/wiki/Differential_invariant https://en.wikipedia.org/wiki/Differential_operator


https://en.wikipedia.org/wiki/Quantum_invariant https://en.wikipedia.org/wiki/Periodic_table_of_topological_invariants

Enumerative invariants

Enumerative invariants:
Sympletic category: Donaldson invariants+ Seiberg–Witten invariants Gromov-Witten invariants
FJRW theory Gopakumar-Vafa invariant

duality miscelanea

Reciprocities: https://en.wikipedia.org/wiki/Quadratic_reciprocity http://en.wikipedia.org/wiki/Weil_reciprocity_for_algebraic_curves http://en.wikipedia.org/wiki/Stanley's_reciprocity_theorem +


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https://en.wikipedia.org/wiki/Topology_(electrical_circuits)#Duality

algebraic geo stuff

https://en.wikipedia.org/wiki/Transfer_principle https://en.wikipedia.org/wiki/Algebraic_geometry_and_analytic_geometry


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category theory


five lemmasix operations


https://en.wikipedia.org/wiki/Universal_property Universal bundle? + https://en.wikipedia.org/wiki/Product_(category_theory) https://en.wikipedia.org/wiki/Exponential_object https://en.wikipedia.org/wiki/Exponential_sheaf_sequence +


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discrete stuff

discrete taylor series discrete taylor series table discrete integration by parts discrete laplacian discrete spectral theory


stackexchange

The Selberg trace formula is making act on , the Frobenius formula is making G act on +


generating functions

Generating functions++connected graph generating function

diferential representations


+https://en.wikipedia.org/wiki/Shift_theorem https://en.wikipedia.org/wiki/Shift_operator https://en.wikipedia.org/wiki/Hasse-Schmidt_derivation


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Sequences

https://en.wikipedia.org/wiki/Category:Spectral_sequences


Surgery exact sequence Serre spectral sequence Mapping_class_group


https://en.wikipedia.org/wiki/Poisson_summation_formula#Derivation

congmatics

https://en.wikipedia.org/wiki/Möbius_transformation


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RPn CPn HPn


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Diagramatics

https://commons.wikimedia.org/wiki/Category:Mathematical_diagrams https://commons.wikimedia.org/wiki/Category:Commutative_diagrams https://commons.wikimedia.org/wiki/Category:Group_theory https://commons.wikimedia.org/wiki/File:Projective-representation-lifting.svg +] + + + + + +

matrices stuff


Khatri rao product


map equivalence

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https://en.wikipedia.org/wiki/Matrix_determinant_lemma#See_also

Gaps

https://en.wikipedia.org/wiki/Gap_theorem_(disambiguation) https://en.wikipedia.org/wiki/Spectral_gap_(physics) https://en.wikipedia.org/wiki/Duality_gap https://en.wikipedia.org/wiki/Prime_gap https://en.wikipedia.org/wiki/Montgomery's_pair_correlation_conjecture https://en.wikipedia.org/wiki/Yang-Mills_existence_and_mass_gap + [3]


spectral stuff

https://en.wikipedia.org/wiki/Singular_integral https://en.wikipedia.org/wiki/Singular_trace

linear algebra


https://en.wikipedia.org/wiki/Matrix_determinant_lemma#See_also + https://en.wikipedia.org/wiki/Matrix_splitting#Matrix_iterative_methods https://en.wikipedia.org/wiki/Matrix_decomposition


https://en.wikipedia.org/wiki/Matrix_pencil


https://en.wikipedia.org/wiki/Rouché-Capelli_theorem


stuff with det,tr


Poisson summation formulaFrobenius reciprocity Selberg trace formula+++++Poisson=Fourier on circle


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https://en.wikipedia.org/wiki/Trigonometric_functions_of_matrices


https://en.wikipedia.org/wiki/Nahm_equations#Nahm-Hitchin_description_of_monopoles https://en.wikipedia.org/wiki/Particle_in_a_one-dimensional_lattice#Kronig-Penney_model


http://mathworld.wolfram.com/Convergent.html


simplex determinant Cayley-Menger_determinant


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https://en.wikipedia.org/wiki/Doubly_periodic_function https://en.wikipedia.org/wiki/Fundamental_pair_of_periods


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https://en.wikipedia.org/wiki/Chern-Simons_theory#HOMFLY_and_Jones_polynomials https://en.wikipedia.org/wiki/Weyl_character_formula#The_SU(2)_case


https://en.wikipedia.org/wiki/Vanishing_theorem


https://en.wikipedia.org/wiki/Analytic_torsion https://en.wikipedia.org/wiki/Crooks_fluctuation_theorem


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for +


https://en.wikipedia.org/wiki/Dedekind_psi_function https://mathoverflow.net/questions/14083/modular-forms-and-the-riemann-hypothesis



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"Index theory"

https://mathoverflow.net/questions/233144/atiyah-singer-theorem-a-big-picture
https://mathoverflow.net/questions/1162/atiyah-singer-index-theorem
http://www.concinnitasproject.org/portfolio/gallery.php?id=Atiyah_Michael


List of fixed-point theorems +





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https://en.wikipedia.org/wiki/Atiyah-Bott_fixed-point_theorem https://en.wikipedia.org/wiki/Supersymmetric_theory_of_stochastic_dynamics#Parisi-Sourlas_approach_to_Langevin_SDEs



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Maximum modulus principle +Fundamental theorem of algebra
Hairy ball theorem real root


https://en.wikipedia.org/wiki/Dividing_a_circle_into_areas#Combinatorics_and_topology_method


Riemann zeta function Hurwitz zeta function Polylogarithm


delete me? 1+2+3+4+... Riemann+Euler-Maclaurin Darboux's formula


Analytic torsion Heat kernel signature


Atiyah Singer index theorem+ Signature operator Equivariant_index theorem


Bott residue formula


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Supersymmetric atiyah Singer index theorem + +?


Equivalences:Abel–Plana_formula<=>Euler–Maclaurin_formula<=>Poisson summation formula


Singular Kernel Regularization


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Algebraic Geometry


https://en.wikipedia.org/wiki/Enriques-Kodaira_classification#Invariants_of_surfaces


https://en.wikipedia.org/wiki/Arithmetic_of_abelian_varieties


Hilbert's basis theorem Hilbert's Nullstellensatz Hilbert's syzygy theorem


https://en.wikipedia.org/wiki/Genus-degree_formula https://en.wikipedia.org/wiki/Plücker_formula https://en.wikipedia.org/wiki/Riemann-Hurwitz_formula


Dual theorems
As the real projective plane, Template:Math, is self-dual there are a number of pairs of well known results that are duals of each other. Some of these are:

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https://mathoverflow.net/a/17139/142708


Hodge duality+->Poincaré duality->Grothendieck local duality->Serre duality poincare-serre connection


https://en.wikipedia.org/wiki/De_Rham_cohomology https://en.wikipedia.org/wiki/Dolbeault_cohomology https://en.wikipedia.org/wiki/Differential_form https://en.wikipedia.org/wiki/Complex_differential_form


kunneth theorem + + +


Riemann-Roch Stuff

Line bundle-Riemann surface Vector Bundle-Complex manifold Quotient stack sheaf-Orbifold Chain-complex sheaf-Scheme Arithmetic+
dimensioncorrection = degreegenus + 1. +
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six operationsImages of sheaves


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https://en.wikipedia.org/wiki/Category:Geometry_of_divisors


https://en.wikipedia.org/wiki/Genus_of_a_multiplicative_sequence

Hodge stuff

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Homotopy stuff

https://math.stackexchange.com/a/3088/683216

algebraic topology


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https://en.wikipedia.org/wiki/Homology_(mathematics)

Topological characteristics of closed 1- and 2-manifolds[1]
Manifold Euler No.
χ
Orientability Betti numbers Torsion coefficient
(1-dimensional)
Symbol[2] Name b0 b1 b2
Circle (1-manifold)   0 Orientable 1 1 N/A N/A
Sphere   2 Orientable 1 0 1 none
Torus   0 Orientable 1 2 1 none
Projective plane   1 Non-orientable 1 0 0 2
Klein bottle   0 Non-orientable 1 1 0 2
2-holed torus −2 Orientable 1 4 1 none
g-holed torus (Genus = g) 2 − 2g Orientable 1 2g 1 none
Sphere with c cross-caps 2 − c Non-orientable 1 c − 1 0 2
2-Manifold with gTemplate:Nbspholes and cTemplate:Nbspcross-caps (cTemplate:Nbsp>Template:Nbsp0) 2Template:NbspTemplate:Nbsp(2gTemplate:Nbsp+Template:Nbspc) Non-orientable 1 (2gTemplate:Nbsp+Template:Nbspc)Template:NbspTemplate:Nbsp1 0 2
NOTES:
  1. For a non-orientable surface, a hole is equivalent to two cross-caps.
  2. Any 2-manifold is the connected sum of g tori and c projective planes. For the sphere , g = c = 0.

geometric algebra

https://en.wikipedia.org/wiki/Geometric_algebra https://en.wikipedia.org/wiki/Comparison_of_vector_algebra_and_geometric_algebra https://en.wikipedia.org/wiki/Rotation_formalisms_in_three_dimensions


https://en.wikipedia.org/wiki/Hodge_star_operator#Derivatives_in_three_dimensions https://en.wikipedia.org/wiki/Exterior_derivative#Exterior_derivative_in_vector_calculus https://en.wikipedia.org/wiki/Closed_and_exact_differential_forms https://en.wikipedia.org/wiki/Exterior_calculus_identities + + ++

sympletic geometry

+ + + !


Differential geo


Maxwell's equations-Alternative formulations Mathematical descriptions of the electromagnetic field P-form electrodynamics


https://en.wikipedia.org/wiki/Category:Theorems_in_Riemannian_geometry


https://en.wikipedia.org/wiki/Laplace_operators_in_differential_geometry
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https://en.wikipedia.org/wiki/Weitzenböck_identity https://en.wikipedia.org/wiki/Bochner's_formula https://en.wikipedia.org/wiki/Bochner_identity


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Minakshisundaram–Pleijel
Lovelock

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Real n-Cauchy-Riemann: +
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Volume form + Connection_form torsion form curvature form + spin connection khäler form + Solder form Conformal connection +


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Degenerancy theory

covering degenerancy manifold degenerancy


Poincaré–Hopf theoremHairy ball theorem


Banach fixed point theorem(existence and uniqueness) Brouwer_fixed-point_theorem(existence) Fixed point degree


Template:Analogous fixed-point theorems
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Hall's marrriage theorem equivalences


Template:Sidebar


Representation stuff

Character theory https://en.wikipedia.org/wiki/Schur_orthogonality_relations https://en.wikipedia.org/wiki/Frobenius-Schur_indicator Weyl character formula Kirillov_character_formula https://en.wikipedia.org/wiki/Dirichlet_character


--SU(2)&SO(3)-- https://en.wikipedia.org/wiki/3D_rotation_group#Connection_between_SO(3)_and_SU(2) https://en.wikipedia.org/wiki/Representation_theory_of_SU(2) https://en.wikipedia.org/wiki/Representation_of_a_Lie_group#An_example:_The_rotation_group_SO(3) https://en.wikipedia.org/wiki/Spin_spherical_harmonics https://en.wikipedia.org/wiki/Clebsch-Gordan_coefficients


https://en.wikipedia.org/wiki/Representation_theory_of_the_symmetric_group https://en.wikipedia.org/wiki/Jucys-Murphy_element


Representation theory Representation of Lie algebra Representation of Lie group Representation of finite groups ℓ-adic representations


https://en.wikipedia.org/wiki/Representation_theorem https://en.wikipedia.org/wiki/Multiplicity-one_theorem


conmutative tuff

prime ideals are maximal if nonzero, i.e. dim D≤1->prime ideals are principal->maximal ideals are principal->gcd(a,b)=1⇒(a,b)=1, i.e. coprime then comaximal->D is Bezout->D is a PID +
++

group stuff

group theory: definitions basics factsnon basic facts


groups: https://en.wikipedia.org/wiki/Bézout's_identity
Rings: https://en.wikipedia.org/wiki/Chinese_remainder_theorem +


burside:+


https://en.wikipedia.org/wiki/Vantieghems_theorem


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+ https://en.wikipedia.org/wiki/Daniel_da_Silva_(mathematician) https://en.wikipedia.org/wiki/Chebotarev_theorem_on_roots_of_unity [4]


Cayley's theorem equivalencesWagner-preston theorem +++


https://en.wikipedia.org/wiki/Deligne-Lusztig_theory


https://en.wikipedia.org/wiki/Zappa–Szép_product
=\=>+ =\=>+ + + ++


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Thompson order formula


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Chebotarev's density theorem[[5] PNTHardy-Ramanujan theorem + + +


Centralizer-Normalizer Orbit stabilizer coset-index


https://en.wikipedia.org/wiki/Wedderburn's_little_theorem https://en.wikipedia.org/wiki/Zappa–Szép_product


Fundamental theorem of abelian groups Fundamental theorem of cyclic groups Fundamental theorem of free groups Jordan–Hölder theorem Finitely generated abelian group Structure theorem for finitely generated modules over a principal ideal domain


https://en.wikipedia.org/wiki/Classification_of_finite_simple_groups https://en.wikipedia.org/wiki/Abelian_group#Classification


mobius table

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mobius+

, ; ,

Lambert




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elliptic stuff

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arithmetic

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Finite unramified extension Finite unramified ring extension Finite extension ++ +

primes stuff

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Digamma functionWeierstrass zeta function


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¿?
https://en.wikipedia.org/wiki/Von_Mangoldt_function




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https://en.wikipedia.org/wiki/Prime_gap https://en.wikipedia.org/wiki/Montgomery's_pair_correlation_conjecture


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https://en.m.wikipedia.org/wiki/Prouhet%E2%80%93Thue%E2%80%93Morse_constant


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Rodrigues's formula Li's criterion


Szegő_limit_theorems Jensen's formula five value theorem Identity theorem


ELSV formula


https://en.wikipedia.org/wiki/Fredholm's theorem Fredholm alternative Farkas_lemma Hyperplane separation theorem Hanh Banach separation theorem Positive-definite matrix Positive-definite kernel Positive definiteness



varieties: Grassman Segre veronese


global-local homology global-local homotopy +


nowhere differentiable: everywhere continuos, nowhere continuos


Moduli stuff

petterson-weil volume+ witten's volume orbifolds volume+ ++

height stuff


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https://en.wikipedia.org/wiki/Height_zeta_function


https://en.wikipedia.org/wiki/Valuation_(algebra) https://mathoverflow.net/questions/310020/summing-bernoulli-numbers


Field Metric Completion zero sequence
Template:Math Template:Math (usual absolute value) R Template:Math
Template:Math obtained using the p-adic valuation, for a prime number Template:Math Template:Math [[p-adic number|Template:Math-adic numbers]] Template:Math
Template:Math (Template:Math any field) obtained using the Template:Math-adic valuation Template:Math Template:Math

+


class number

Arithmetic geometry Fermat's squares theorem Minkowski's theorem + Gauss circle problem Dirichlet's divisor problem


Class field theory Class number Class number formula
List of number fields with class number one Lists of discriminants of class number 1+ Minkowski's bound
Stark-Heegner_theorem Heegner number Kronecker-Weber_theorem Kummer theory Fundamental discriminant
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elliptic and quadratics

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+ Template:L-functions-footer Template:Prime number conjectures


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Perron's formulaShimura correspondence


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Winding number-Eisenbud Levine Khimshiashvili signature formula


Roth's_theorem-Duffin-Schaeffer conjecture


Kutsenov trace formula-Gutzwiller trace formula[6]


Min-Max theoremMax-min_inequality


Kolmogorov equation-Fokker Planck equation
Koopman operator-Perron-Frobenius operator


not recursive function not computable function not ZFC-dependent function bound+


tuple primes

+


Euler product + +


Feller-Tornier constant + Pólya conjecture Chebyshev's bias + + Goldfeld conjecture + Parity_problem


+ Artin's conjecture +


+


k-tuple conjecture+ Bateman-Horn conjecture+


+ https://en.wikipedia.org/wiki/Montgomery's_pair_correlation_conjecture https://en.wikipedia.org/wiki/Sato-Tate_conjecture + +


square free distribution +


hypergeometric stuff


Painlevé's conditionsMalmquist's conditions++


Legendre form hypergeometric differential equation
weierstrass form Picard–Fuchs differential equation
Riemann form Riemann's differential equation

??????????????? Gauss-Manin connection


https://en.wikipedia.org/wiki/Confluent_hypergeometric_function



hipergeometric equation (3 singularities) Heun's equation (4 singularities) Heine-Stieltjes polynomials(n singularities) Schwarz's list



Poincaré series Igusa zeta function


Hyperbolic geometryHyperbolic manifold++


{5,5}-tilling-Poincaré Sphere+


Minimal program model +


Abel's theorem converse Abel's theorem


Associahedron Pemutohedron


https://en.wikipedia.org/wiki/Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain


Template:Commutative ring classes Template:Hidden begin Template:Algebraic structures Template:Hidden end


eta stuff

Eta invariant Dirichlet_eta_function Spectral asymmetry Witten index
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heat table

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q q q
q

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https://en.wikipedia.org/wiki/Hecke_operator https://en.wikipedia.org/wiki/Witt_vector




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convergence stuff

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https://en.wikipedia.org/wiki/Operator_topologies


https://en.wikipedia.org/wiki/Pasting_lemma


Littlewood's three principles of real analysis
Hahn-Banach theorem Open mapping theorem Uniform boundedness principle
Closed graph theorem Bounded inverse theorem zabreikos lemma +
https://en.wikipedia.org/wiki/Template:Functional_analysis
https://en.wikipedia.org/wiki/Category:Theorems_in_functional_analysis


Riesz representation theorem Herglotz-Riesz representation Riesz–Markov–Kakutani representation theorem
Spectral theorem


https://en.wikipedia.org/wiki/Monotone_convergence_theorem https://en.wikipedia.org/wiki/Dominated_convergence_theorem


Katětov–Tong insertion theorem


Riesz-Fischer theoremHopf–Rinow theorem


https://en.wikipedia.org/wiki/Category:Theorems_in_approximation_theory
https://en.wikipedia.org/wiki/Stone-Weierstrass_theorem https://en.wikipedia.org/wiki/Fejér's_theorem + +
https://en.wikipedia.org/wiki/Runge's_phenomenon https://en.wikipedia.org/wiki/Gibbs_phenomenon


https://en.wikipedia.org/wiki/Morera's_theorem https://en.wikipedia.org/wiki/Localization_theorem


as=>p=>d+ homeomorphism preserving properties


as p d
LLN T T T
LIL F T T
CLT F F T

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Pointwise continuity x x x
Uniform continuity x x
equicontinuity x x
Uniform equicontinuity x

Continuously differentiable Lipschitz continuousα-Hölder continuousuniformly continuousContinuous function=continuous

Lipschitz continuousabsolutely continuousbounded variationdifferentiablealmost everywhere
+


https://en.wikipedia.org/wiki/Modes_of_convergence_(annotated_index) +


LLN,LIL,CLT

LIL random matrix

PNT,RH,EK


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https://mathoverflow.net/questions/6889/what-is-the-difference-between-a-zeta-function-and-an-l-function

Geodesics PGT+ Selberg zeta function selberg trace formula
P-adic P-adic L-function
Motives Motivic zeta function Motivic L-function
Varietes Weil Conjectures++ Local zeta function Hasse-Weil zeta function+
Schemes Grand RH¿? arithmetic zeta function
Ideals ERH Dedekind zeta function
Characters GRH Dirichlet L-function
Naturals RH PNT Riemann zeta Explicit_formulae

Selberg class Abstract analytic number theory

PNT RH


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Counting LLN CLT Zeros
naturals primes PNT RH
naturals factors Hardy ramanujan Erdős-Kac_theorem
Geodesics primes PGT ++
Geodesics factors ?
Elliptic curves factors ?

+


+ + One can view Selberg’s theorem as a sort of Fourier-analytic variant of the Erdös-Kac theorem.
PNT scaled models+ + +
mertens=/=PNT+ +


CLT

Martingale CLT Functional integralPath integral