Hirzebruch L-polynomials and multiple zeta values

TL;DR

This paper links the coefficients of Hirzebruch L-polynomials to alternating multiple zeta values, revealing non-zero coefficients for all monomials in Pontryagin classes and similar results for A-hat genus polynomials.

Contribution

It establishes a novel connection between characteristic polynomial coefficients and multiple zeta values, providing explicit expressions and sign patterns.

Findings

Coefficients of Hirzebruch L-polynomials expressed via alternating multiple zeta values

All monomials in Pontryagin classes have non-zero coefficients with expected signs

Similar results obtained for A-hat genus polynomials

Abstract

We express the coefficients of the Hirzebruch L-polynomials in terms of certain alternating multiple zeta values. In particular, we show that every monomial in the Pontryagin classes appears with a non-zero coefficient, with the expected sign. Similar results hold for the polynomials associated to the A-hat genus.