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.
Organisers: Holly Green, Besfort Shala
Comments are closed.