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Elliptic units for complex cubic fields

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  • UserLuis GarcĂ­a (UCL)
  • ClockTuesday 14 May 2024, 14:30-15:30
  • HouseMR13.

If you have a question about this talk, please contact Jef Laga.

The elliptic Gamma function—an elliptic version of the ordinary Gamma function—is a meromorphic special function in three variables that mathematical physicists have shown to satisfy modular functional equations under SL(3, Z). In this talk I will present evidence (numerical and theoretical) that products of values of this function are often algebraic numbers 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. The talk will be based on arxiv:2311.04110 and is joint work with Nicolas Bergeron and Pierre Charollois.

This talk is part of the Number Theory Seminar series.

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