Hecke eigenvalues and relations for Siegel Eisenstein series of arbitrary degree, level, and character

Lynne H Walling

doi:10.1142/S179304211750021X

Hecke eigenvalues and relations for Siegel Eisenstein series of arbitrary degree, level, and character

Lynne H Walling^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

7 Citations (Scopus)

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Abstract

We evaluate the action of Hecke operators on Siegel Eisenstein series of arbitrary degree, level and character. For square-free level, we simultaneously diagonalize the space with respect to all the Hecke operators, computing the eigenvalues explicitly, and obtain a multiplicity-one result. For arbitrary level, we simultaneously diagonalize the space with respect to the Hecke operators attached to primes not dividing the level, again computing the eigenvalues explicitly.

Original language	English
Pages (from-to)	325-370
Number of pages	46
Journal	International Journal of Number Theory
Volume	13
Issue number	2
Early online date	18 Aug 2016
DOIs	https://doi.org/10.1142/S179304211750021X
Publication status	Published - Mar 2017

Keywords

Hecke eigenvalues
Eisenstein series
Siegel modular forms

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N2 - We evaluate the action of Hecke operators on Siegel Eisenstein series of arbitrary degree, level and character. For square-free level, we simultaneously diagonalize the space with respect to all the Hecke operators, computing the eigenvalues explicitly, and obtain a multiplicity-one result. For arbitrary level, we simultaneously diagonalize the space with respect to the Hecke operators attached to primes not dividing the level, again computing the eigenvalues explicitly.

AB - We evaluate the action of Hecke operators on Siegel Eisenstein series of arbitrary degree, level and character. For square-free level, we simultaneously diagonalize the space with respect to all the Hecke operators, computing the eigenvalues explicitly, and obtain a multiplicity-one result. For arbitrary level, we simultaneously diagonalize the space with respect to the Hecke operators attached to primes not dividing the level, again computing the eigenvalues explicitly.

KW - Hecke eigenvalues

KW - Eisenstein series

KW - Siegel modular forms

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DO - 10.1142/S179304211750021X

M3 - Article (Academic Journal)

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EP - 370

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 2

ER -

Hecke eigenvalues and relations for Siegel Eisenstein series of arbitrary degree, level, and character

Abstract

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