On the Wiener-Wintner theorem for nilsequences

TL;DR

This paper provides a Fourier analytic proof of the Wiener-Wintner theorem's generalization for nilsequences, including explicit bounds on the limits of weighted ergodic averages, advancing understanding in ergodic theory.

Contribution

It offers a new Fourier analytic proof of the Host-Kra generalization of the Wiener-Wintner theorem with explicit bounds on ergodic average limits.

Findings

Fourier analytic proof of the generalized Wiener-Wintner theorem

Explicit bounds on the limits of weighted ergodic averages

Enhanced understanding of nilsequence behavior in ergodic theory

Abstract

We give a Fourier analytic proof of the generalisation due to Host and Kra of the classical Wiener-Wintner theorem and give some explicit bounds on the limit of the weighted ergodic averages.