Lower bounds for moments of L-functions: symplectic and orthogonal examples

TL;DR

This paper establishes lower bounds for the magnitude of moments of L-functions within orthogonal and symplectic families, providing evidence for conjectured behaviors in these families.

Contribution

It offers the first rigorous lower bounds matching the conjectured order of magnitude for moments of L-functions in orthogonal and symplectic families.

Findings

Lower bounds align with conjectured magnitudes

Supports conjectures about L-function moments

Advances understanding of L-function behavior

Abstract

We give lower bounds of the conjectured order of magnitude for an orthogonal and a symplectic family of L-functions.