Applications of Wirtinger inequalities on the distribution of zeros of the Riemann zeta-function

Abstract

On the hypothesis that the (2k) th moments of the Hardy Z -function are correctly predicted by random matrix theory and the moments of the derivative of Z are correctly predicted by the derivative of the characteristic polynomials of unitary matrices, we establish new large spaces between the zeros of the Riemann zeta-function by employing some Wirtinger-type inequalities. In particular, it is obtained that (15) ≥ 6.1392 which means that consecutive nontrivial zeros often differ by at least 6.1392 times the average spacing. Copyright © 2010 Samir H. Saker.