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Talk 7: On Eisenstein's Jugendtraum for complex cubic fields (online talk)

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Nicolas Bergeron
ENS Paris
Thu, 09/03/2023 - 11:15 - 12:15
MPIM Lecture Hall

The /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 mathematical physicists have shown to satisfy modular functional equations under SL(3,Z). In this talk I will try to convince you that this function, and some avatars of it, can be used to extend the theory of complex multiplication to complex cubic fields. In an on-going joint work with Pierre Charollois and Luis Garcia, we indeed propose a conjectural solution to Hilbert's 12th problem for (cubic) almost totally real fields and we give a lot of numerical evidences that support this conjecture.

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