The spin -function on for Siegel modular forms

Published

Journal Article

We give a Rankin–Selberg integral representation for the Spin (degree eight) $L$-function on $\operatorname{PGSp}_{6}$ that applies to the cuspidal automorphic representations associated to Siegel modular forms. If $\unicode[STIX]{x1D70B}$ corresponds to a level-one Siegel modular form $f$ of even weight, and if $f$ has a nonvanishing maximal Fourier coefficient (defined below), then we deduce the functional equation and finiteness of poles of the completed Spin $L$-function $\unicode[STIX]{x1D6EC}(\unicode[STIX]{x1D70B},\text{Spin},s)$ of $\unicode[STIX]{x1D70B}$.

Full Text

Duke Authors

Cited Authors

  • Pollack, A

Published Date

  • July 2017

Published In

Volume / Issue

  • 153 / 7

Start / End Page

  • 1391 - 1432

Published By

Electronic International Standard Serial Number (EISSN)

  • 1570-5846

International Standard Serial Number (ISSN)

  • 0010-437X

Digital Object Identifier (DOI)

  • 10.1112/s0010437x17007114

Language

  • en