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SUMMARY:Luis Garcia (University College London)
DTSTART:20240409T210000Z
DTEND:20240409T220000Z
DTSTAMP:20260423T024838Z
UID:UAANTS/88
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/88/">
 Elliptic units for complex cubic fields</a>\nby Luis Garcia (University Co
 llege London) as part of University of Arizona Algebra and Number Theory S
 eminar\n\n\nAbstract\nThe elliptic Gamma function — a generalization of 
 the q-Gamma function\, which is itself the q-analog of the ordinary Gamma 
 function — is a meromorphic special function in several variables that m
 athematical physicists have shown to satisfy modular functional equations 
 under SL(3\,Z). In this talk I will present evidence (numerical and theore
 tical) that products of values of this function are often algebraic number
 s that satisfy explicit reciprocity laws and are related to derivatives of
  Hecke L-functions of cubic fields at s=0. We will discuss the relation to
  Stark's conjectures and will see that this function conjecturally allows 
 to extend the theory of complex multiplication to complex cubic fields as 
 envisioned by Hilbert's 12th problem. This is joint work with Nicolas Berg
 eron and Pierre Charollois.\n
LOCATION:https://researchseminars.org/talk/UAANTS/88/
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