A conjecture on Whittaker-Fourier coefficients of cusp forms

TL;DR

This paper proposes a new conjecture relating Whittaker-Fourier coefficients of automorphic forms to existing conjectures, refining previous predictions in the context of quasi-split reductive groups.

Contribution

It formulates an analogue of the Ichino-Ikeda conjecture specifically for Whittaker-Fourier coefficients, sharpening Sakellaridis-Venkatesh conjectures.

Findings

Formulation of a new conjecture for Whittaker-Fourier coefficients

Refinement of Sakellaridis-Venkatesh conjectures

Connections established with Ichino-Ikeda conjectures

Abstract

We formulate an analogue of the Ichino-Ikeda conjectures for the Whittaker-Fourier coefficients of automorphic forms on quasi-split reductive groups. This sharpens the conjectures of Sakellaridis-Venkatesh in the case at hand.