The Chowla-Selberg formula for quartic Abelian CM fields

Cass, Robert

doi:10.1090/proc/12935

The Chowla-Selberg formula for quartic Abelian CM fields
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by Robert Cass PDF

Proc. Amer. Math. Soc. 144 (2016), 2753-2769 Request permission

Abstract:

We provide explicit evaluations of the Chowla-Selberg formula for quartic abelian CM fields due to Barquero-Sanchez and Masri. These identities relate values of a Hilbert modular function at CM points to values of Euler’s gamma function $\Gamma$ and an analogous function $\Gamma _2$ at rational numbers. Our work consists of two main parts. First, we implement an algorithm in SageMath to compute the CM points. Second, we exhibit families of quartic abelian CM fields for which the part of the formula involving values of $\Gamma$ and $\Gamma _2$ takes a particularly simple form.

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