On the zeros of functions from the extended Selberg class of degree 0

Abstract

We give an improved upper bound for the error term in the Riemann-von Mangoldt formula for functions of degree 0 in the extended Selberg class. The bound is uniform for functions with no zeros in a certain half-plane. The first such bound was given by J. Kaczorowski and A. Pereili [3] in the proof that the extended Selberg class is a semigroup with factorization.