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- ...of modular forms describes the algebraic structure of the space of modular forms. ...[vector space]] of modular forms of weight {{mvar|k}}. The ring of modular forms of {{math|Γ}} is the graded ring <math display="inline">M(\Gamma) = \bigopl ...8 KB (1,193 words) - 08:16, 30 October 2024
- {{DISPLAYTITLE:Modular forms modulo ''p''}} ...x modular forms and the [[p-adic modular form|''p''-adic theory of modular forms]]. ...9 KB (1,480 words) - 00:28, 18 May 2024
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- {{distinguish|almost holomorphic modular form}} ...lowed to have poles at cusps. Examples include [[modular function]]s and [[modular form]]s. ...2 KB (281 words) - 16:02, 13 October 2023
- In mathematics, a '''Siegel theta series''' is a [[Siegel modular form]] associated to a positive definite [[Lattice (discrete subgroup)|latt ...attice|unimodular]] then this is a Siegel modular form for the full Siegel modular group. ...1 KB (165 words) - 07:36, 27 June 2024
- ...r form]]s is another modular form, generalizing the product of two modular forms. ...ions for [[polynomial]]s in [[derivative]]s of modular forms to be modular forms, and {{harvs|txt|last=Cohen|authorlink=Henri Cohen (number theorist)|year=1 ...3 KB (520 words) - 19:55, 4 June 2024
- {{distinguish|Weakly holomorphic modular form}} ...hic modular form E<sub>2</sub>(τ) – 3/πIm(τ)), and derivatives of modular forms. ...4 KB (596 words) - 14:28, 4 September 2020
- ...een [[modular form]]s ''F'' of half integral weight ''k''+1/2, and modular forms ''f'' of even weight 2''k'', discovered by {{harvs|txt|authorlink=Goro Shim is a holomorphic [[modular function]] with weight ''2k'' and character <math>\chi^2</math> . ...2 KB (285 words) - 22:53, 27 February 2024
- ...wa lift''' (or '''lifting''') takes [[elliptic modular form]]s to [[Siegel modular form]]s of degree 2. The existence of this lifting was conjectured in 1977 ...dular forms ''f'' of weight 2''k'' − 2 to level 1 Siegel modular forms of degree 2 and weight ''k''. The L-functions (when ''f'' is a Hecke eigenf ...3 KB (489 words) - 02:09, 12 March 2023
- {{Short description|The slash operator is highly relevant to modular forms and is not currently included in Wikipedia.}} The '''slash operator''' in the context of [[modular form]]s is a fundamental tool used to define the action of matrices on thes ...5 KB (724 words) - 05:16, 29 November 2024
- ...–Moody algebra]]s. Meromorphic Jacobi forms appear in the theory of [[Mock modular form]]s. ...r | first1=Martin | last2=Zagier | first2=Don | title=The theory of Jacobi forms | publisher=Birkhäuser Boston | location=Boston, MA | series=Progress in Ma ...2 KB (284 words) - 16:31, 5 February 2022
- ...Siegel series''') is a generalization of [[Eisenstein series]] to [[Siegel modular form]]s. ...rices ''C'',''D'' that are the "bottom half" of an element of the [[Siegel modular group]]. ...1 KB (169 words) - 00:50, 13 February 2019
- ...f a Siegel upper half plane in which case the theta constants are [[Siegel modular form]]s. The [[theta function of a lattice]] is essentially a special case [[Category:Automorphic forms]] ...2 KB (345 words) - 00:09, 10 November 2024
- ...ning simultaneous Hecke eigenform with modular group SL(2,'''Z''')) is a [[modular form]] which is an [[eigenvector]] for all [[Hecke operator]]s ''T<sub>m</s ...nstein series]]. Another example is the [[Weierstrass's elliptic functions#Modular discriminant|Δ function]]. ...3 KB (438 words) - 00:56, 31 July 2024
- ...orm]] of weight 2''k'' for Γ. Note that, when Γ is the full [[modular group]] and ''n'' = 0, one obtains the Eisenstein series of weigh ...ion | last1=Kollár | first1=János | title=Shafarevich maps and automorphic forms | publisher=[[Princeton University Press]] | series=M. B. Porter Lectures | ...3 KB (425 words) - 20:43, 10 May 2018
- ...rphism]] of commutative ring spectra [[MString]] →'''[[Topological modular forms|tmf]]'''. ...du/~pgoerss/papers/Exp.1005.P.Goerss.pdf |chapter=1005 Topological Modular Forms <nowiki>[after Hopkins, Miller, and Lurie]</nowiki> |title=Séminaire Bourba ...2 KB (251 words) - 18:20, 31 July 2024
- ...of modular forms describes the algebraic structure of the space of modular forms. ...[vector space]] of modular forms of weight {{mvar|k}}. The ring of modular forms of {{math|Γ}} is the graded ring <math display="inline">M(\Gamma) = \bigopl ...8 KB (1,193 words) - 08:16, 30 October 2024
- {{DISPLAYTITLE:Modular forms modulo ''p''}} ...x modular forms and the [[p-adic modular form|''p''-adic theory of modular forms]]. ...9 KB (1,480 words) - 00:28, 18 May 2024
- {{short description|Siegel modular form}} In mathematics, a '''Klingen Eisenstein series''' is a [[Siegel modular form]] of weight ''k'' and degree ''g'' depending on another Siegel cusp fo ...2 KB (284 words) - 19:22, 23 July 2024
- ...[[algebraic curve]]s. Furthermore, it has applications to the theory of [[modular form]]s on [[reductive group|reductive]] [[algebraic groups]]<ref>{{Citatio | contribution=Siegel modular forms and their applications ...3 KB (363 words) - 15:59, 30 June 2019
- ...n sums he was able to derive estimates for Fourier coefficients of modular forms in cases where [[Pierre Deligne]]'s proof of the [[Weil conjectures]] was n ...| last1=Kuznecov | first1=N. V. | title=The Petersson conjecture for cusp forms of weight zero and the Linnik conjecture. Sums of Kloosterman sums |mr=5689 ...3 KB (378 words) - 04:09, 4 November 2020
- ...a [[mock modular form]]. Let <math>E_2(z)</math> denote the weight 2 quasi-modular [[Eisenstein series]] and let <math>\eta(z)</math> denote the [[Dedekind et is a [[mock modular form]] of weight 3/2 on the full [[modular group]] <math>SL_2(\mathbb{Z})</math> with multiplier system <math>\chi_{\e ...3 KB (385 words) - 05:24, 4 August 2024
- ...s a kind of orthogonality relation between coefficients of a holomorphic [[modular form]]. It is a specialization of the more general [[Kuznetsov trace formul ...an [[orthonormal basis]] of <math>S_k(\Gamma(1))</math>, the space of cusp forms of weight <math>k>2</math> on <math>SL_2(\mathbb{Z})</math>. Then for any p ...1 KB (211 words) - 20:50, 31 March 2023