STM Journals Peer-reviewed research from Consortium e-Learning Network

Research & Reviews: Discrete Mathematical Structures

On the Riemann Hypothesis in The Light of The Littlewood Criterion of Equivalence

  1. Lukasz Andrzej Glinka

Abstract

In 1859, Riemann extended the Euler study onto the case of a complex variable according to then new Cauchy's complex analysis. According to his point of view, all non-trivial zeros of the Riemann zeta function are located on the critical line s=1/2+it, where t is a real number. In 1912, Littlewood presented the equivalence criterion for the Riemann Hypothesis based on the Mertens function. In this paper, the Riemann Hypothesis is discussed and this is shown that the Littlewood criterion can be immediately applied for proving the Riemann Hypothesis, according to the analytic number theory.

Keywords

Support