Hiroyuki Yoshida

Periods and the multiple gamma function in the archimedean case

The Chowla-Selberg formula expresses the period of an elliptic curve with CM by division values of the gamma function. I will talk on a (conjectural) generalization of this formula: The periods of an abelian variety with CM can be expressed by division values of the multiple gamma function. The most interesting features are: Our conjecture concerns the next term to the leading term of the Taylor expansion of an L-function. A subtle factorization process is involved to obtain the formula. We can view the Stark-Shintani conjecture from the higher stand point.