Explicitly realizing average Siegel theta series as linear combinations of Eisenstein series

Lynne H Walling

doi:10.1007/s11139-017-9973-7

Explicitly realizing average Siegel theta series as linear combinations of Eisenstein series

Lynne H Walling^*

^*Corresponding author for this work

School of Mathematics

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

4 Citations (Scopus)

246 Downloads (Pure)

Abstract

We find nice representatives for the 0-dimensional cusps of the degree n Siegel upper half-space under the action of Γ0(N). To each of these, we attach a Siegel Eisenstein series, and then we make explicit a result of Siegel, realizing any integral weight average Siegel theta series of arbitrary level N and Dirichlet character χL modulo N as a linear combination of Siegel Eisenstein series.

Original language	English
Number of pages	25
Journal	Ramanujan Journal
Early online date	8 Feb 2018
DOIs	https://doi.org/10.1007/s11139-017-9973-7
Publication status	E-pub ahead of print - 8 Feb 2018

Keywords

Eisenstein series
Quadratic forms
Siegel modular forms
Theta series

Access to Document

10.1007/s11139-017-9973-7

Full-text PDF (accepted author manuscript)
This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Springer at https://link.springer.com/article/10.1007%2Fs11139-017-9973-7 . Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 377 KB

Handle.net

Persistent link

Cite this

@article{dfd5fc9ab116441e9fb4afcb8fc34ff1,

title = "Explicitly realizing average Siegel theta series as linear combinations of Eisenstein series",

abstract = "We find nice representatives for the 0-dimensional cusps of the degree n Siegel upper half-space under the action of Γ0(N). To each of these, we attach a Siegel Eisenstein series, and then we make explicit a result of Siegel, realizing any integral weight average Siegel theta series of arbitrary level N and Dirichlet character χL modulo N as a linear combination of Siegel Eisenstein series.",

keywords = "Eisenstein series, Quadratic forms, Siegel modular forms, Theta series",

author = "Walling, \{Lynne H\}",

year = "2018",

month = feb,

day = "8",

doi = "10.1007/s11139-017-9973-7",

language = "English",

journal = "Ramanujan Journal",

issn = "1382-4090",

publisher = "Springer Netherlands",

}

TY - JOUR

T1 - Explicitly realizing average Siegel theta series as linear combinations of Eisenstein series

AU - Walling, Lynne H

PY - 2018/2/8

Y1 - 2018/2/8

N2 - We find nice representatives for the 0-dimensional cusps of the degree n Siegel upper half-space under the action of Γ0(N). To each of these, we attach a Siegel Eisenstein series, and then we make explicit a result of Siegel, realizing any integral weight average Siegel theta series of arbitrary level N and Dirichlet character χL modulo N as a linear combination of Siegel Eisenstein series.

AB - We find nice representatives for the 0-dimensional cusps of the degree n Siegel upper half-space under the action of Γ0(N). To each of these, we attach a Siegel Eisenstein series, and then we make explicit a result of Siegel, realizing any integral weight average Siegel theta series of arbitrary level N and Dirichlet character χL modulo N as a linear combination of Siegel Eisenstein series.

KW - Eisenstein series

KW - Quadratic forms

KW - Siegel modular forms

KW - Theta series

UR - https://www.scopus.com/pages/publications/85041546879

UR - https://arxiv.org/abs/1702.06494

U2 - 10.1007/s11139-017-9973-7

DO - 10.1007/s11139-017-9973-7

M3 - Article (Academic Journal)

AN - SCOPUS:85041546879

SN - 1382-4090

JO - Ramanujan Journal

JF - Ramanujan Journal

ER -

Explicitly realizing average Siegel theta series as linear combinations of Eisenstein series

Abstract

Keywords

Access to Document

Handle.net

Other files and links

Fingerprint

Cite this