New relations on zeta and $L$ functions

TL;DR

This paper establishes new mathematical relations involving the Riemann zeta function at even integers and Dirichlet L-functions at odd integers, using calculus techniques like Taylor series and partial fractions.

Contribution

It introduces novel relations on zeta and L-functions at specific arguments, leveraging calculus methods not previously applied in this context.

Findings

Derived new relations for zeta at even arguments

Established relations for Dirichlet L-functions at odd arguments

Utilized calculus techniques such as Taylor series and partial fractions

Abstract

We prove new relations on zeta function at even arguments and Dirichlet $L$ function at odd. The key idea is to make use of the Taylor series and partial fraction decomposition of cotangent and secant functions as we discuss in calculus and complex analysis.