A Refined Random Matrix Model for Function Field L-Functions

June 4, 2024
Since work of Montgomery and Katz-Sarnak, the eigenvalues of random matrices have been used to model the zeroes of the Riemann zeta function and other L-functions. Keating and Snaith extended this to also model the distribution of values of the L-functions. This should allow predictions of the moments, but predictions for moments derived from the Keating-Snaith model do not match their known values. A modified random matrix model due to Gonek, Hughes, and Keating predicts the leading term of known formulas for the moments but not the lower-order terms. In, for now, the function field case, I propose a different modification of the random matrix model. In work in progress, I show this model predicts all terms of the moment formula when q is sufficiently large.