Rankin–Selberg L-functions and “beyond endoscopy”

Authors

Satadal Ganguly, Indian Statistical Institute, Kolkata
Ramdin Mawia, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Mathematische Zeitschrift

Abstract

Let f and g be two holomorphic cuspidal Hecke eigenforms on the full modular group SL 2(Z). We show that the Rankin–Selberg L-function L(s, f× g) has no pole at s= 1 unless f= g, in which case it has a pole with residue 3π(4π)kΓ(k)‖f‖2, where ‖ f‖ is the Petersson norm of f. Our proof uses the Petersson trace formula and avoids the Rankin–Selberg method.

First Page

175

Last Page

184

DOI

10.1007/s00209-019-02431-5

Publication Date

10-1-2020

Recommended Citation

Ganguly, Satadal and Mawia, Ramdin, "Rankin–Selberg L-functions and “beyond endoscopy”" (2020). Journal Articles. 129.
https://digitalcommons.isical.ac.in/journal-articles/129