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SUMMARY:Amanda Folsom (Amherst College)
DTSTART:20201202T160000Z
DTEND:20201202T170000Z
DTSTAMP:20260423T021420Z
UID:hnts/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/hnts/16/">Ei
 senstein series\, cotangent-zeta sums\, knots\, and quantum modular forms<
 /a>\nby Amanda Folsom (Amherst College) as part of Heilbronn number theory
  seminar\n\n\nAbstract\nQuantum modular forms\, defined in the rational nu
 mbers\, transform like modular forms do on the upper half-plane\, up to su
 itably analytic error functions. In this talk we give frameworks for two d
 ifferent examples of quantum modular forms originally due to Zagier: the D
 edekind sum\, and a certain q-hypergeometric sum due to Kontsevich. For th
 e first\, we extend work of Bettin and Conrey and define twisted Eisenstei
 n series\, study their period functions\, and establish quantum modularity
  of certain cotangent-zeta sums. For the second\, we discuss results due t
 o Hikami\, Lovejoy\, the author\, and others\, on quantum modular and quan
 tum Jacobi forms related to colored Jones polynomials for certain families
  of knots.\n
LOCATION:https://researchseminars.org/talk/hnts/16/
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