Study odd numbers with traditional functions

TL;DR

This paper explores the relationships between odd numbers and classical functions such as the gamma, Riemann zeta, and von Mangoldt functions, analyzing their convergence within number theory.

Contribution

It introduces new connections between odd numbers and traditional functions, along with convergence analysis of related series.

Findings

Identifies specific relationships between odd numbers and classical functions

Analyzes convergence properties of series derived from these relationships

Provides insights into number theory applications

Abstract

In this paper we will focus on the study of relationships that can exist between odd numbers and different traditional functions like the gamma function, Riemann zeta function or function of von Mangoldt. Number theory applies to this study. It will also analyze the convergence of the series obtained as a result of that relationship.