The Langlands-Shahidi method over function fields: Ramanujan Conjecture and Riemann Hypothesis for the unitary groups

TL;DR

This paper extends the Langlands-Shahidi method to function fields, proving key functoriality results for unitary groups, with significant implications for the Ramanujan Conjecture and Riemann Hypothesis.

Contribution

It develops the Langlands-Shahidi method over characteristic p fields and establishes functoriality for unitary groups, advancing understanding of automorphic forms and L-functions.

Findings

Proved the Langlands-Shahidi method over function fields.

Established functoriality for unitary groups to GL(n).

Implications for Ramanujan Conjecture and Riemann Hypothesis.

Abstract

We establish the Langlands-Shahidi method over a global field of characteristic p. We then focus on the unitary groups and prove global and local Langlands functoriality to general linear groups for generic representations. Main applications are to the Ramanujan Conjecture and Riemann Hypothesis.