Seminars & Colloquia Calendar

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Special Colloquium

Moments of families of L-functions

Matthew Young (Texas A&M)

Location:  Hill 705
Date & time: Wednesday, 20 December 2023 at 3:30PM - 4:30PM

The study of moments of the Riemann zeta function was initiated over a century ago by Hardy and Littlewood and continues to be an active area of research.  This topic has broadened to encompass moments of other families of L-functions, and one of the important themes has been understanding connections and analogies between different families, as well as conjectural links with random matrix theory.  One of the oldest and most fundamentally important analogies concerns the Riemann zeta function on the one side, and Dirichlet L-functions on the other side.  As a concrete example, one can see this comparison as relating primes in short intervals and in arithmetic progressions.  These analogies serve as a powerful guiding principle but in practice it can be very difficult to make them mathematically rigorous.  I will describe a few recent advances in this subject that help equalize our understanding of Dirichlet L-functions in comparison with the Riemann zeta function. This talk will survey this area of research, and is intended for a broad audience.

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