Some observations concerning the distribution of the zeros of the zeta functions, III

Abstract

1. Introduction. The purpose of the present article is to give a refinement on our previous results (e.g. Theorems 6 and 7 in pp. 141-142 of [4] and a special case of Theorem in p. 100 of [1]) on the exponential sums over the zeros of some zeta functions. Some of the consequences resulting from this will also be mentioned.