Two-point correlation function for Dirichlet L-functions

Abstract

The two-point correlation function for the zeros of Dirichlet L-functions at a height E on the critical line is calculated heuristically using a generalization of the Hardy-Littlewood conjecture for pairs of primes in arithmetic progression. The result matches the conjectured Random-Matrix form in the limit as $E\to \infty$ and, importantly, includes finite-E corrections. These finite-E corrections differ from those in the case of the Riemann zeta-function, obtained in (1996 Phys. Rev. Lett. 77 1472), by certain finite products of primes which divide the modulus of the primitive character used to construct the L-function in question.

10 pages

Cited by in corpus (2)

• A method for calculating spectral statistics based on random-matrix universality with an application to the three-point correlations of the Riemann zeros
• Hilbert-Pólya Conjecture, Zeta-Functions and Bosonic Quantum Field Theories