j-invariant and Borcherds Phi-function

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• Shu Kawaguchi (Doshisha University)
• Tuesday 15 October 2019, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jack Thorne.

The j-invariant is the SL_2(Z)-invariant holomorphic function on the complex upper half-plane, which is fundamental in many branches of mathematics. Besides the j-invariant itself, the difference of j-invariants have beautiful properties such as Gross—Zagier’s result on singular moduli and the denominator formula for the monster Lie algebra. In this talk, we explain that the difference of j-invariants is closely related to the Borcherds Phi-function, an automorphic form on the period domain for Enriques surfaces characterizing the discriminant divisor. This is joint work with Shigeru Mukai and Ken-Ichi Yoshikawa, and we use an algebraic expression of the Borcherds Phi-function obtained in our previous paper.

This talk is part of the Number Theory Seminar series.

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