On the order of the Titchmarsh's sum in the theory of the Riemann zeta-function and on the biquadratic effect in the information theory

TL;DR

This paper solves the classical problem of determining the order of Titchmarsh's sum and explores its connection to the Kotelnikoff-Whittaker-Nyquist theorem in information theory, revealing new links between number theory and information theory.

Contribution

It provides a solution to the longstanding problem on the order of Titchmarsh's sum and establishes a novel connection with fundamental principles in information theory.

Findings

Solved the classical problem on the order of Titchmarsh's sum.

Established a link between Titchmarsh's sum and the Kotelnikoff-Whittaker-Nyquist theorem.

Revealed a biquadratic effect in the context of information theory.

Abstract

We obtain in this paper the solution of the classical problem on the order of the Titchmarsh's sum (1934). Simultaneously, we obtain a connection of this problem and the Kotelnikoff-Whittaker-Nyquist's theorem from the information theory.