The elliptic gamma function and Stark units

Abstract: I will present a conjecture extending the classical theory of elliptic units from imaginary quadratic fields to complex cubic fields. The role played by theta functions in the classical construction now corresponds to the elliptic gamma function, a meromorphic function arising in mathematical physics. Using this function we will define complex numbers that we conjecture to lie on specified abelian extensions of cubic fields and to satisfy explicit reciprocity laws. I will discuss some numerical and theoretical evidence for these claims.

The talk will be based on arXiv:2311.04110 and is joint work with Nicolas Bergeron and Pierre Charollois.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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