We discuss a nilsequence version of the classical Wiener-Wintner theorem on convergence of weighted ergodic averages due to Host and Kra and present a uniform version of this result. This is a joint work with Pavel Zorin-Kranich.
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[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/node/3444
[3] http://www.mpim-bonn.mpg.de/node/5079
[4] http://www.mpim-bonn.mpg.de/node/5312
[5] http://www.mpim-bonn.mpg.de/webfm_send/289/1
[6] http://www.mpim-bonn.mpg.de/webfm_send/289