Autocorrelation of ratios of L-functions

Abstract

We give a new heuristic for all of the main terms in the quotient of products of L-functions averaged over a family. These conjectures generalize the recent conjectures for mean values of L-functions. Comparison is made to the analogous quantities for the characteristic polynomials of matrices averaged over a classical compact group.

Minor corrections

References in corpus (3)

• Products and Ratios of Characteristic Polynomials of Random Hermitian Matrices
• A Symplectic Test of the L-Functions Ratios Conjecture
• Howe pairs, supersymmetry, and ratios of random characteristic polynomials for the unitary groups U(N)

Cited by in corpus (3)

• On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class
• A representation theory approach to integral moments of L-functions over function fields
• Determining Optimal Test Functions for Bounding the Average Rank in Families of $L$-Functions