Whittaker functions on GL(4,R) and archimedean Bump--Friedberg integrals

TL;DR

This paper provides explicit formulas for Whittaker functions on GL(4,R) for all irreducible generic representations and identifies test vectors that realize the associated L-factors in Bump-Friedberg integrals.

Contribution

It introduces explicit formulas for Whittaker functions on GL(4,R) and determines test vectors for Bump-Friedberg integrals, advancing understanding of automorphic L-functions.

Findings

Explicit formulas for Whittaker functions on GL(4,R)

Identification of test vectors for L-factors

Application to Bump-Friedberg integrals

Abstract

We give explicit formulas of Whittaker functions on GL(4,R) for all irreducible generic representations. As an application, we determine test vectors which attain the associated L-factors for Bump-Friedberg integrals on GL(4,R).