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SUMMARY:Bounds for Kloosterman Sums for $\\mathrm{GL}_n$ [MPIM]
DTSTART:20250226T133000Z
DTEND:20250226T143000Z
DTSTAMP:20260716T205200Z
UID:indico-event-234@math-events.uni-bonn.de
DESCRIPTION:Speakers: Johannes Linn (MPIM)\n\nNumber theory lunch seminar\
 nClassical Kloosterman sums defined by $S(m\,n\;c):=\\sum_{x\\in (\\mathbb
 {Z}/c\\mathbb{Z})^*}e\\Big(\\frac{mx+n\\overline{x}}{c}\\Big)$ for $m\,n\\
 in\\mathbb{Z}$ and $c\\in\\mathbb{Z}^+$ have become ubiquitous in Number T
 heory appearing for example in Fourier coefficients of classical Poincaré
  series and therefore in the geometric side of relative trace formulae of 
 Petersson-Kuznetsov type.Working with relative trace formulae over $\\math
 rm{GL}_n$ requires understanding of more general Kloosterman sums.In this 
 talk\, I will present a method to parametrize and bound the generalized Kl
 oosterman sums for $\\mathrm{GL}_n$ obtaining a power saving compared to t
 he trivial bound.\n\nhttps://math-events.uni-bonn.de/event/234/
LOCATION:MPIM\, Vivatsgasse\,  7 - Lecture Hall (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/234/
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