Differentiating polynomials, and zeta(2)

TL;DR

This paper explores the derivatives of polynomials with equally spaced zeros and uncovers connections to the values of the Riemann zeta-function at positive even integers, revealing new mathematical relationships.

Contribution

It introduces novel links between polynomial derivatives and zeta(2), advancing understanding of their mathematical interplay.

Findings

Derived explicit formulas relating polynomial derivatives to zeta(2)

Established new connections between polynomial zeros and zeta-function values

Provided insights into the structure of derivatives of polynomials with equally spaced zeros

Abstract

We study the derivatives of polynomials with equally spaced zeros and find connections to the values of the Riemann zeta-function at the positive even integers.