Riemann-type functional equations: Dirichlet polynomial approximations and a weak Gram law
Volume 204 / 2022
Acta Arithmetica 204 (2022), 97-113
MSC: Primary 11M06; Secondary 30D35.
DOI: 10.4064/aa210111-13-4
Published online: 20 June 2022
Abstract
We study Riemann-type functional equations with respect to value-distribution theory and derive implications for their solutions. In particular, we improve upon results of Bombieri and Friedlander on Dirichlet polynomial approximations to $L$-functions and we prove that a generalized weak Gram law for the degree-one elements of the extended Selberg class is true infinitely often.
