Communications in Number Theory and Physics

Volume 2 (2008)

Number 3

Autocorrelation of ratios of $L$-functions

Pages: 593 – 636



Brian Conrey (American Institute of Mathematics, Palo Alto, Calif.)

David W. Farmer (American Institute of Mathematics, Palo Alto, Calif.)

Martin R. Zirnbauer (Institut für Theoretische Physik, Universität zu Koeln, Germany)


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

Published 1 January 2008