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SUMMARY:Alia Hamieh
DTSTART:20230405T140000Z
DTEND:20230405T150000Z
DTSTAMP:20260422T102440Z
UID:FGC-IPM/32
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FGC-IPM/32/"
 >Moments of $L$-functions and Mean Values of Long Dirichlet Polynomials</a
 >\nby Alia Hamieh as part of FGC-HRI-IPM Number Theory Webinars\n\n\nAbstr
 act\nEstablishing asymptotic formulae for moments of $L$-functions is a ce
 ntral theme in analytic number theory. This topic is related to various no
 n-vanishing conjectures and the generalized Lindelöf Hypothesis. A major 
 breakthrough in analytic number theory occurred in 1998 when Keating and S
 naith established a conjectural formula for moments of the Riemann zeta fu
 nction using ideas from random matrix theory. The methods of Keating and S
 naith led to similar conjectures for moments of many families of $L$-funct
 ions. These conjectures have become a driving force in this field which ha
 s witnessed substantial progress in the last two decades. \nIn this talk\,
  I will review the history of this subject and survey some recent results.
  I will also discuss recent joint work with Nathan Ng on the mean values o
 f long Dirichlet polynomials which could be used to model moments of the z
 eta function.\n\nZoom Meeting ID: 856 1386 0958 Passcode: 513992\n
LOCATION:https://researchseminars.org/talk/FGC-IPM/32/
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