Explicit formula for a fundamental class of functions

Abstract

The purpose of this paper is to prove an analogue of A. Weil's explicit formula for a fundamental class of functions, i.e. the class of meromorphic functions that have an Euler sum representation and satisfy certain a functional equation. The advance of this explicit formula is that it enlarges the class of allowed test functions, from the class of functions with bounded Jordan variation to the class of functions of $\phi $-bounded variation. A condition posed to the test function at zero is also reconsidered.