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Department of Pure Mathematics and Mathematical Statistics

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.

Further information

Time:

15Oct
Oct 15th 2019
14:30 to 15:30

Venue:

MR13

Speaker:

Shu Kawaguchi (Doshisha University)

Series:

Number Theory Seminar