English

Two-point correlation function for Dirichlet L-functions

Mathematical Physics 2015-06-16 v1 math.MP

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 EE\rightarrow\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.

Keywords

Cite

@article{arxiv.1307.6010,
  title  = {Two-point correlation function for Dirichlet L-functions},
  author = {E. Bogomolny and J. P. Keating},
  journal= {arXiv preprint arXiv:1307.6010},
  year   = {2015}
}

Comments

10 pages

R2 v1 2026-06-22T00:56:09.406Z