# 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 $\unicode[STIX]{x1D70B}$.

• Pollack, A

• July 2017

• 153 / 7

• 1391 - 1432

• 1570-5846

• 0010-437X

### Digital Object Identifier (DOI)

• 10.1112/s0010437x17007114

• en