### Generalised moments, large deviations, and numerics of $L$-functions and characteristic polynomials

Linfoot Number Theory Seminar

12th May 2021, 4:00 pm – 5:00 pm

Fry Building, Online

I'll present results on generalised moments and large deviations for the random matrix groups associated with the symmetry classes for families of $L$-functions. Such a connection is motivated by the work of Keating and Snaith, Katz and Sarnak, etc. In particular, one can connect number theoretic functions and characteristic polynomials to a third structure: branching random walks. I'll review this theory and present some theoretical and numerical results. Additionally, motivated by a conjecture of Radziwi{\l}{\l}, we demonstrate a large deviation result in the moderate regime for unitary characteristic polynomials which has implications for large zeta values.

Collaborators include L-P. Arguin, T. Assiotis, and J. P. Keating.

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