Hecke operators on Hilbert-Siegel theta series

Dan Fretwell; Lynne Walling

doi:10.1142/S179304212150072X

Hecke operators on Hilbert-Siegel theta series

Dan Fretwell^*, Lynne Walling

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the action of Hecke-type operators on Hilbert-Siegel theta series attached to lattices of even rank. We show that the average Hilbert-Siegel theta series are eigenforms for these operators, and we explicitly compute the eigenvalues.

Original language	English
Pages (from-to)	1965-1996
Number of pages	32
Journal	International Journal of Number Theory
Volume	17
Issue number	9
DOIs	https://doi.org/10.1142/S179304212150072X
Publication status	Published - 1 Oct 2021
Externally published	Yes

Keywords

quadratic forms
Theta series
totally real fields

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10.1142/S179304212150072XLicence: Unspecified

Cite this

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title = "Hecke operators on Hilbert-Siegel theta series",

abstract = "We consider the action of Hecke-type operators on Hilbert-Siegel theta series attached to lattices of even rank. We show that the average Hilbert-Siegel theta series are eigenforms for these operators, and we explicitly compute the eigenvalues. ",

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author = "Dan Fretwell and Lynne Walling",

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AU - Walling, Lynne

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N2 - We consider the action of Hecke-type operators on Hilbert-Siegel theta series attached to lattices of even rank. We show that the average Hilbert-Siegel theta series are eigenforms for these operators, and we explicitly compute the eigenvalues.

AB - We consider the action of Hecke-type operators on Hilbert-Siegel theta series attached to lattices of even rank. We show that the average Hilbert-Siegel theta series are eigenforms for these operators, and we explicitly compute the eigenvalues.

KW - quadratic forms

KW - Theta series

KW - totally real fields

U2 - 10.1142/S179304212150072X

DO - 10.1142/S179304212150072X

M3 - Article

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SN - 1793-0421

VL - 17

SP - 1965

EP - 1996

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 9

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Hecke operators on Hilbert-Siegel theta series

Abstract

Keywords

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Cite this