Extension of Wiener-Wintner double recurrence theorem to polynomials

TL;DR

This paper extends the Wiener-Wintner double recurrence theorem to include polynomial cases, broadening its applicability in ergodic theory and recurrence phenomena.

Contribution

It introduces a generalization of the Wiener-Wintner theorem to polynomial sequences, advancing understanding of recurrence in dynamical systems.

Findings

Successfully generalized the theorem to polynomial sequences

Established new recurrence results for polynomial cases

Enhanced theoretical framework for ergodic recurrence

Abstract

We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.