On the use of the generalized Littlewood theorem concerning integrals of the logarithm of analytical functions for calculations of infinite sums and analysis of zeroes of analytical functions

TL;DR

This paper applies a generalized Littlewood theorem to evaluate infinite sums and analyze zeros of analytical functions, providing new insights related to the Riemann hypothesis.

Contribution

It introduces novel applications of the generalized Littlewood theorem for calculating sums and studying zeros, advancing analytical techniques in complex analysis.

Findings

Derived new criteria related to the Riemann hypothesis

Calculated specific infinite sums using the theorem

Analyzed properties of zeros of analytical functions

Abstract

Recently, we have established and used the generalized Littlewood theorem concerning contour integrals of the logarithm of analytical function to obtain a few new criteria equivalent to the Riemann hypothesis. Here, the same theorem is applied to calculate certain infinite sums and study the properties of zeroes of a few analytical functions.