# 東京理科大学理工学部 数学科

seminar:2015:002

### 第02回

• 講演者 : 志賀 弘典 氏（千葉大学）
• 題目 : Modular functions on the 2-dimensional hyperball with application to number theory
• 日時 : 平成27年5月15日（金）16:40 – 17:30

The elliptic modular function $j(\tau)$ is an automorphic function on the complex upper half plane $\bf H$ with respect to the modular group ${\it SL}_2 ({\bf Z})$. It has many applications to number theory. Starting from the hypergeometric function of 2-variables, we can construct explicit modular functions on ${\bf B}^2$ (the 2-dimensional hyper ball). They are called Picard modular functions. It is one typical way to have 2-dimensional analogs of $j(\tau)$, another one is the Hilbert modular function. In this talk we explain one Picard modular function and its application to the complex multiplication theory of higher degree.

seminar/2015/002.txt · 最終更新: 2017/11/16 18:27 (外部編集)