题目： Modular forms and Jacobi’s four squares problem
报告人：何伟 (数学学院11级)
时间：10月10日（星期五）16：30-17：30
（16：00-16：30下午茶）
地点：第二报告厅
摘要：A modular form is a holomorphic function on the complex upper half plane satisfying a certain kind of functional equation with respect to the group action of the modular group (Z). The theory of modular forms belongs to complex analysis but the main importance of the theory has traditionally been in its connections with number theory. In the 1950’s Taniyama made the famous conjecture, all rational elliptic curves arise from modular forms, which plays a crucial role in the proof of the Fermat’s Last Theory. In this lecture, I’ll give some very basic definitions and properties of a modular form and its application to solve the Jacobi’s four squares problem, to find the total number of ways a given positive integer n can be represented as the sum of four squares.
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