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Modular form

In number theory and complex analysis, a modular form is a type of function of a complex number variable that possesses a high degree of symmetry, of a certain kind. Similarly to a periodic function of a real variable, a modular form repeats or transforms in a certain way when its argument is subjected to a particular transformation. Unlike an ordinary…

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Overview

Definition

Modular functions

Geometric interpretation

Rings of modular forms

Types

Generalizations

History

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Map overview Semantic statistics

Modular form

Nodes125
Edges124
Triples104
Avg. degree1.98
Density0.016
Components1

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Modular form

Top relations

related to References · 52
Modular form → Adèle Groups, Annals, Apostol, Arithmetic, Automorphic Forms, BF01394347Behold Modular Forms, Bibcode, Cambridge, Cambridge University Press, Chapter VII, Course, Dirichlet Series, Erich, Fifth Fundamental Operation, First Course, Fred, Gelbart, Graduate Texts, Göttingen, Hecke
related to Modular forms for more general groups · 9
Modular form → Again, For, In, Mk, Similarly, Sk, SL, The, The C-vector
related to Rings of modular forms · 9
Modular form → For, Gamma, In, Michael Rapoport, Mk, Pierre Deligne, Rings, SL, Such
related to Line bundles · 7
Modular form → By, Hodge, In, Kodaira, Modular, Spencer, Symbolically
related to Definition · 5
Modular form → Automorphy, Gamma, Im, In, SL
related to history · 4
Modular form → By Erich Hecke, Felix Klein, In, The
related to Lattice and elliptic-curve interpretation · 4
Modular form → If, The, Zz, Zα
related to New forms · 4
Modular form → Gamma, New, The, These
is a · 3
Modular form → holomorphic function on the complex upper half-plane that roughly satisfies a functional equation with respect to the group action of the modular group and a growth condition, special case of an automorphic form, type of function of a complex number variable that possesses a high degree of symmetry
related to Cusp forms · 2
Modular form → For, Fourier

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Important terminology

modular forms function form functions displaystyle weight condition number theory cusp group called holomorphic sl meromorphic complex elliptic also one

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Modular formis atype of function of a complex number variable that possesses a high degree of symmetry0.90text
Modular formis aholomorphic function on the complex upper half-plane that roughly satisfies a functional equation with respect to the group action of the modular group and a growth condition0.90text
Modular formis aspecial case of an automorphic form0.90text
replacing a complex number z byinstance ofits symmetries include transformations0.80text
the Dedekind eta functioninstance ofFunctions0.80text
a modular form of weight 1/2instance ofFunctions0.80text
may be encompassed by the theory by allowing automorphic factorsinstance ofFunctions0.80text
Modular formrelated to Cusp formsFor0.60section
Modular formrelated to Cusp formsFourier0.60section
Modular formrelated to DefinitionIn0.60section
Modular formrelated to DefinitionSL0.60section
Modular formrelated to DefinitionGamma0.60section

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