DATE2022-04-21 16:10-17:00

PLACE數學系館 1F3174教室

SPEAKER魏福村 教授(國立清華大學數學系

TITLECM Periods and Special Gamma Values

ABSTRACT 因疫情狀況改為線上
The gamma function is one commonly used extension of the factorial function to complex numbers. It shows up in various research areas, and the special values of which are closely related to “CM periods”. The celebrated Chowla-Selberg formula expresses the periods of elliptic curves with “complex multiplications” in terms of a very beautiful monomial combinations of gamma values at fractions. In fact, the recipe comes precisely from the “Stickelberger” evaluators of Dirichlet L-values. This “Chowla-Selberg phenomenon” is regarded as a geometric aspect of the Kronecker-Weber theorem for abelian extensions of the rational number field, which is studied extensively for CM periods in the higher dimensional cases based on the work of Weil, Shimura, Deligne, Gross, Anderson, Colmez, etc.
In this talk, we shall start from basic properties of the gamma function, and then discuss algebraic relations among special gamma values and their “Chowla-Selberg” connections with CM periods. A brief summary of my current progress on a “positive-characteristic” analogue will be mentioned if time permits.
會議號: 2519 820 0310
會議密碼: 5Mnqp7BeCG8