✦ LIBER ✦

Hecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular forms

✍ Scribed by Alexandru Ghitza

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 549 KB
Volume: 106
Category: Article
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2003.12.009

No coin nor oath required. For personal study only.

✦ Synopsis

In his letter (Israel J. Math. 95 (1996) 281), Serre proves that the systems of Hecke eigenvalues given by modular forms ðmod pÞ are the same as the ones given by locally constant functions A Â B =B Â -F p ; where B is the endomorphism algebra of a supersingular elliptic curve. We generalize this result to Siegel modular forms, proving that the systems of Hecke eigenvalues given by Siegel modular forms ðmod pÞ of genus g are the same as the ones given by algebraic modular forms ðmod pÞ on the group GU g ðBÞ; as defined in Gross (Math. Res. Notices (16) (1998) 865; Israel J. Math. 113 (1999) 61). The correspondence is obtained by restricting to the superspecial locus of the moduli space of abelian varieties.

📜 SIMILAR VOLUMES

Congruences for eigenvalues of Hecke ope

Congruences for eigenvalues of Hecke operators on Siegel modular forms of degree two

✍ Shin-ichiro Mizumoto 📂 Article 📅 1986 🏛 Springer 🌐 English ⚖ 548 KB

Siegel modular forms of degree two: Heck

Siegel modular forms of degree two: Hecke eigenforms

✍ Erik A. Lippa 📂 Article 📅 1974 🏛 Springer 🌐 English ⚖ 249 KB

Explicit Action of Hecke Operators on Si

Explicit Action of Hecke Operators on Siegel Modular Forms

✍ James Lee Hafner; Lynne H Walling 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 182 KB

We develop an algorithm for determining an explicit set of coset representatives (indexed by lattices) for the action of the Hecke operators T(p), T j (p 2 ) on Siegel modular forms of fixed degree and weight. This algorithm associates each coset representative with a particular lattice W, pL ı W ı

On convolutions of Siegel modular forms

✍ Özlem Imamoğlu; Yves Martin 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 289 KB

## Abstract In this article we study a Rankin‐Selberg convolution of __n__ complex variables for pairs of degree __n__ Siegel cusp forms. We establish its analytic continuation to ℂ^__n__^, determine its functional equations and find its singular curves. Also, we introduce and get similar results f

An Analogy of Bol's Result on Jacobi For

An Analogy of Bol's Result on Jacobi Forms and Siegel Modular Forms

✍ Youngju Choie; Haesuk Kim 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 104 KB

In this paper, the analogy of Bol's result to the several variable function case is discussed. One shows how to construct Siegel modular forms and Jacobi forms of higher degree, respectively, using Bol's result.

Skew-holomorphic Jacobi forms of index 1

Skew-holomorphic Jacobi forms of index 1 and Siegel modular forms of half-integral weight

✍ Shuichi Hayashida 📂 Article 📅 2004 🏛 Elsevier Science 🌐 English ⚖ 279 KB

The isomorphism between Kohnen's plus space and Jacobi forms of index 1 was given by Eichler-Zagier. In this article, we generalize this isomorphism for higher degree in the case of skew-holomorphic Jacobi forms.

Hecke eigenvalues of Siegel modular forms (mod&#xa0;p) and of algebraic modular forms

✦ Synopsis

Hecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular forms