The Chowla-Selberg formula for abelian CM fields and Faltings heights
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| Authors: | , |
|---|---|
| Format: | artículo original |
| Publication Date: | 2016 |
| Description: | In this paper we establish a Chowla-Selberg formula for abelian CM fields. This is an identity which relates values of a Hilbert modular function at CM points to values of Euler’s gamma function Γ and an analogous function Γ2 at rational numbers. We combine this identity with work of Colmez to relate the CM values of the Hilbert modular function to Faltings heights of CM abelian varieties. We also give explicit formulas for products of exponentials of Faltings heights, allowing us to study some of their arithmetic properties using the Lang-Rohrlich conjecture. |
| Country: | Kérwá |
| Institution: | Universidad de Costa Rica |
| Repositorio: | Kérwá |
| OAI Identifier: | oai:kerwa.ucr.ac.cr:10669/76495 |
| Online Access: | https://www.cambridge.org/core/journals/compositio-mathematica/article/chowlaselberg-formula-for-abelian-cm-fields-and-faltings-heights/0EEE0C3B5124C8CB191C427F98FC3CC5 https://hdl.handle.net/10669/76495 |
| Access Level: | acceso abierto |
| Keyword: | Chowla-Selberg formula CM point Faltings height Hilbert modular function |