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Better than squareroot cancellation for multiplicative functions

Recent developments in Analytic Number Theory May 01, 2017 - May 05, 2017

May 01, 2017 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Adam Harper (University of Warwick)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • mobius function

  • Dirichlet characters

  • multiplicative chaos

  • random multiplicative function

  • complex analysis

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Harper

Abstract

It is a standard heuristic that sums of oscillating number theoretic functions, like the M\"obius function or Dirichlet characters, should exhibit squareroot cancellation. It is often very difficult to prove anything as strong as that, and we generally expect that if we could prove squareroot cancellation it would be the best possible bound. I will discuss recent results showing that, in fact, certain averages of multiplicative functions exhibit a bit more than squareroot cancellation

Supplements
28389?type=thumb Haper.Notes 838 KB application/pdf Download
Video/Audio Files

Harper

H.264 Video 1-Harper.mp4 488 MB video/mp4 rtsp://videos.msri.org/data/000/028/284/original/1-Harper.mp4 Download
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