Ergodic Theory and Dynamical Systems

Uniformity in the polynomial Wiener–Wintner theorem

a1 Einstein Drive, Institute for Advanced Study, Princeton, NJ 08540, USA (e-mail:

Article author query
frantzikinakis n   [Google Scholar] 


In 1993, E. Lesigne proved a polynomial extension of the Wiener–Wintner theorem and asked two questions: does this result have a uniform counterpart and can an assumption of total ergodicity be replaced by ergodicity? The purpose of this article is to answer these questions, the first one positively and the second one negatively.

(Published Online July 10 2006)
(Received January 5 2006)
(Revised February 27 2006)