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Gross's proof of the Chowla-Selberg formula

Posted by Martin Orr on Friday, 04 March 2016 at 11:40

Today I am going to write about Gross's proof of the Chowla-Selberg formula (up to algebraic numbers). As I discussed last time, the Chowla-Selberg formula is a formula for the periods of a CM elliptic curve E in terms of values of the gamma function. The idea of Gross's proof is to construct a family of abelian varieties equipped with a section of the de Rham cohomology which has constant periods, such that there is one abelian variety in the family where the period is easy to calculate, and another abelian variety in the family is a power of E and so knowing a period of this variety allows us to calculate the periods of E.

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