TY - JOUR

T1 - Two-point correlation function for Dirichlet L-functions

AU - Bogomolny, E.

AU - Keating, J. P.

PY - 2013/3/8

Y1 - 2013/3/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84874131234&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/46/9/095202

DO - 10.1088/1751-8113/46/9/095202

M3 - Article (Academic Journal)

AN - SCOPUS:84874131234

VL - 46

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 9

M1 - 095202

ER -