English

A uniform nilsequence Wiener-Wintner theorem for bilinear ergodic averages

Dynamical Systems 2015-08-06 v2

Abstract

We show that a kk-linear pointwise ergodic theorem on an ergodic measure-preserving system implies a uniform kk-linear nilsequence Wiener-Wintner theorem on that system. The assumption is known to hold for arbitrary systems and k=2k=2 (due to Bourgain) and for distal systems and arbitrary kk (due to Huang, Shao, and Ye).

Keywords

Cite

@article{arxiv.1504.04647,
  title  = {A uniform nilsequence Wiener-Wintner theorem for bilinear ergodic averages},
  author = {Pavel Zorin-Kranich},
  journal= {arXiv preprint arXiv:1504.04647},
  year   = {2015}
}

Comments

v2: 4 pages, characterization of good weights for L^2 convergence added, uniformity seminorm in the main result corrected

R2 v1 2026-06-22T09:18:09.835Z