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UID:00827a0a35c0b7110641634d8e09b2e1
CATEGORIES:Number Theory Seminar
CREATED:20260205T193515
SUMMARY:Special functions and building Kuznetsov formulas on GL(n)
LOCATION:HLL 525
DESCRIPTION:Abstract:\nMany of the constructions of analytic number theory generalize f
 rom the classical GL(2) objects (like modular/Maass forms, Kloosterman sums
 , and L-functions) to GL(n), and studying these new objects involves specia
 l functions on GL(n) (like Bessel functions, zonal spherical functions, and
  Whittaker functions).  I'll discuss several of these new functions and the
 ir roles in constructing Kuznetsov-type trace formulas.\nThe past few years
 , I've been on a quest to find integral representations for the Bessel func
 tions occurring in the GL(n) Kuznetsov formula.  We have these for GL(2), G
 L(3) and now GL(4) and I think I know how to construct them for GL(n).  I'l
 l discuss the spectral families on GL(n) and their corresponding Kuznetsov 
 formulas.  Finally, I'll talk about the integral representations we want fo
 r the Bessel functions and how (I hope) they lead to applications like Weyl
  laws, moments and subconvexity of L-functions.\n
X-ALT-DESC;FMTTYPE=text/html:<p style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (West Euro
 pean)', -apple-system, 'system-ui', Roboto, 'Helvetica Neue', sans-serif; f
 ont-size: 15px; font-style: normal; font-weight: 400; letter-spacing: norma
 l; orphans: 2; text-indent: 0px; text-transform: none; widows: 2; word-spac
 ing: 0px; white-space: normal; text-align: left; margin: 0px;"><span data-o
 lk-copy-source="MessageBody" style="border: 0px; font-style: inherit; font-
 variant: inherit; font-weight: inherit; font-size: 12pt; line-height: inher
 it; font-family: Aptos, sans-serif; margin: 0px; padding: 0px; vertical-ali
 gn: baseline;">Abstract:</span></p><p style="color: #242424; font-family: '
 Segoe UI', 'Segoe UI Web (West European)', -apple-system, 'system-ui', Robo
 to, 'Helvetica Neue', sans-serif; font-size: 15px; font-style: normal; font
 -weight: 400; letter-spacing: normal; orphans: 2; text-indent: 0px; text-tr
 ansform: none; widows: 2; word-spacing: 0px; white-space: normal; text-alig
 n: left; margin: 0px;"><span style="border: 0px; font-style: inherit; font-
 variant: inherit; font-weight: inherit; font-size: 12pt; line-height: inher
 it; font-family: Aptos, sans-serif; margin: 0px; padding: 0px; vertical-ali
 gn: baseline;">Many of the constructions of analytic number theory generali
 ze from the classical GL(2) objects (like modular/Maass forms, Kloosterman 
 sums, and L-functions) to GL(n), and studying these new objects involves sp
 ecial functions on GL(n) (like Bessel functions, zonal spherical functions,
  and Whittaker functions).&nbsp; I'll discuss several of these new function
 s and their roles in constructing Kuznetsov-type trace formulas.</span></p>
 <p style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (West Euro
 pean)', -apple-system, 'system-ui', Roboto, 'Helvetica Neue', sans-serif; f
 ont-size: 15px; font-style: normal; font-weight: 400; letter-spacing: norma
 l; orphans: 2; text-indent: 0px; text-transform: none; widows: 2; word-spac
 ing: 0px; white-space: normal; text-align: left; margin: 0px;"><span style=
 "border: 0px; font-style: inherit; font-variant: inherit; font-weight: inhe
 rit; font-size: 12pt; line-height: inherit; font-family: Aptos, sans-serif;
  margin: 0px; padding: 0px; vertical-align: baseline;">The past few years, 
 I've been on a quest to find integral representations for the Bessel functi
 ons occurring in the GL(n) Kuznetsov formula.&nbsp; We have these for GL(2)
 , GL(3) and now GL(4) and I think I know how to construct them for GL(n).&n
 bsp; I'll discuss the spectral families on GL(n) and their corresponding Ku
 znetsov formulas.&nbsp; Finally, I'll talk about the integral representatio
 ns we want for the Bessel functions and how (I hope) they lead to applicati
 ons like Weyl laws, moments and subconvexity of L-functions.</span></p>
CONTACT:Jack Buttcane
DTSTAMP:20260826T215140
DTSTART;TZID=America/New_York:20260210T140000
DTEND;TZID=America/New_York:20260210T150000
SEQUENCE:0
TRANSP:OPAQUE
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