Two-point correlation function for Dirichlet L-functions

E. Bogomolny*, J. P. Keating

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

7 Citations (Scopus)


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 → ∞ and, importantly, includes finite-E corrections. These finite-E corrections differ from those in the case of the Riemann zeta-function, obtained in Bogomolny and Keating (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.

Original languageEnglish
Article number095202
JournalJournal of Physics A: Mathematical and Theoretical
Issue number9
Publication statusPublished - 8 Mar 2013

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