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SUMMARY:Lillian Pierce (Duke University)
DTSTART:20210415T210000Z
DTEND:20210415T220000Z
DTSTAMP:20260423T035823Z
UID:JNTS/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/JNTS/21/">ON
  BURGESS BOUND AND SUPERORTHOGONALITY</a>\nby Lillian Pierce (Duke Univers
 ity) as part of Columbia CUNY NYU number theory seminar\n\n\nAbstract\nThe
  Burgess bound is a well-known upper bound for short multiplicative charac
 ter sums\, with a curious proof. It implies\, for example\, a subconvexity
  bound for Dirichlet L-functions. In this talk we will present two types o
 f new work on Burgess bounds. First\, we will describe new Burgess bounds 
 in multi-dimensional settings. Second\, we will present a new perspective 
 on Burgess's method of proof. Indeed\, in order to try to improve a method
 \, it makes sense to understand the bigger “proofscape” in which a met
 hod fits. We will show that it can be regarded as an application of supero
 rthogonality. This perspective turns out to unify many topics ranging acro
 ss harmonic analysis and number theory. We will survey these connections\,
  with a focus on the number-theoretic side.\n
LOCATION:https://researchseminars.org/talk/JNTS/21/
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