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Speaker:

Masanobu Kaneko
Affiliation:

Kyushu University
Date:

Tue, 2017-05-23 09:00 - 09:50
Location:

MPIM Lecture Hall
Parent event:

Conference "Modular forms are everywhere" The generating function of traces of singular moduli of the modular j-invariant

becomes a modular form of weight 3/2. This is Don's celebrated discovery, inspired

by a work of R. Borcherds. Using this modular form, one can obtain a formula for

the Fourier coefficients of the modular j-invariant in terms of singular moduli.

In this talk, I shall review these works, and introduce recent developments

regarding an application of the formula (due to R. Murty and K. Sampath)

as well as generalizations (due to T. Matsusaka).

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