On the global Gan–Gross–Prasad conjecture for general spin groups

Melissa Emory

Vol. 306 (2020), No. 1, 115–151

DOI: 10.2140/pjm.2020.306.115

Abstract

We formulate a global Gan–Gross–Prasad conjecture for general spin groups. That is, we formulate a conjecture on a relation between periods of certain automorphic forms on ${GSpin}_{n+1}\times {GSpin}_n$ along the diagonal subgroup ${GSpin}_n$ and some $L$-values. To support the conjecture, we show that the conjecture holds for $n=2$ and $3$ and for certain cases for $n=4$.

Keywords

periods of automorphic forms, $L$-values, Gan–Gross–Prasad conjecture

Mathematical Subject Classification 2010

Primary: 11F70

Secondary: 22E55

Milestones

Received: 19 February 2019

Revised: 22 October 2019

Accepted: 12 December 2019

Published: 14 June 2020