On the Distribution of the non-trivial Roots of Riemann's Zeta Function. An alternative Approach

Abstract

Expressing Weierstrass type infinite products in terms of Stieltjes integrals is discussed. The asymptotic behavior of particular types of infinite products is compared against the asymptotic behavior of the entire function Xi(s), well-known in Riemann zeta function theory. An approximate formula for the distribution of the non-trivial roots of Riemann's zeta function is obtained.