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SUMMARY:Elliptic units for complex cubic fields - Luis García (UCL)
DTSTART:20240514T133000Z
DTEND:20240514T143000Z
UID:TALK215638@talks.cam.ac.uk
CONTACT:Jef Laga
DESCRIPTION:The elliptic Gamma function -- an elliptic version of the ordi
 nary Gamma function -- is a meromorphic special function in three variable
 s that mathematical physicists have shown to satisfy modular functional eq
 uations under SL(3\, Z). In this talk I will present evidence (numerical a
 nd theoretical) that products of values of this function are often algebra
 ic numbers that satisfy explicit reciprocity laws and are related to deriv
 atives 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 conjectura
 lly allows to extend the theory of complex multiplication to complex cubic
  fields as envisioned by Hilbert's 12th problem. The talk will be based on
  arxiv:2311.04110 and is joint work with Nicolas Bergeron and Pierre Charo
 llois.\n\n
LOCATION:MR13
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