The Chowla-Selberg formula for quartic Abelian CM fields
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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.References
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Additional Information
- Robert Cass
- Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
- Email: robert.cass@uky.edu
- Received by editor(s): June 9, 2015
- Published electronically: March 22, 2016
- Communicated by: Ken Ono
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2753-2769
- MSC (2010): Primary 11F41; Secondary 11R42
- DOI: https://doi.org/10.1090/proc/12935
- MathSciNet review: 3487212