Mathematical Research Letters

Volume 24 (2017)

Number 1

On the Rankin–Selberg integral of Kohnen and Skoruppa

Pages: 173 – 222



Aaron Pollack (Department of Mathematics, Stanford University, Stanford, California, U.S.A.)

Shrenik Shah (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)


The Rankin–Selberg integral of Kohnen and Skoruppa produces the $\mathrm{Spin} \: L$-function for holomorphic Siegel modular forms of genus two. In this paper, we reinterpret and extend their integral to apply to arbitrary cuspidal automorphic representations of $\mathrm{PGSp}_4$. We show that the integral is related to a non-unique model and analyze it using the approach of Piatetski–Shapiro and Rallis.

A.P. has been partially supported by NSF grant DMS-1401858. S.S. has been supported in parts through NSF grants DGE-1148900, DMS-1401967, and also through the Department of Defense (DoD) National Defense Science & Engineering Graduate Fellowship (NDSEG) Program.

Received 14 February 2015

Accepted 5 February 2016

Published 7 June 2017