Themes of parity in the valuation for integer numbers of the zeta function and of five related functions

TL;DR

This paper explores the valuation of the Riemann zeta function and five related functions at integer points, linking the problem to parity themes through an elementary approach suitable for student understanding.

Contribution

It introduces a simple, accessible method connecting valuation problems to parity concepts, making a partially open problem more approachable for learners.

Findings

Connects valuation of functions to parity themes

Provides an elementary approach for educational purposes

Relates function parity to integer argument properties

Abstract

This paper considers the problem of the valuation for integer numbers of the zeta function and of five other functions which are naturally associated to it. A relatively elementary approach is exposed, which closely connects this still partially open problem to five themes of parity: the notions of parity of a function and of parity of the degree of a polynomial are here related to the distinctions of parity concerning the natural argument of the six considered functions as well as the integer numbers of which some inverse powers are summed. The adopted method essentially aims at enabling the students in mathematics to have an entry into this problem.