The Chowla-Selberg formula for abelian CM fields and Faltings heights Academic Article

abstract

• In this paper we establish a ChowlaSelberg formula for abelian CM fields. This is an identity which relates values of a Hilbert modular function at CM points to values of Eulers gamma function ${
  mGamma}$ and an analogous function ${
  mGamma}_{2}$ 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 LangRohrlich conjecture.

authors

• Masri, Mohamad

published proceedings

• COMPOSITIO MATHEMATICA

author list (cited authors)

• Barquero-Sanchez, A., & Masri, R.

citation count

• 1

publication date

• March 2016

publisher

• Wiley  Publisher

keywords

• Chowla-selberg Formula
• Cm Point
• Faltings Height
• Hilbert Modular Function

Digital Object Identifier (DOI)

• 10.1112/S0010437X15007629

start page

• 445

end page

• 476

volume

• 152

issue

• 3

URL

• http://dx.doi.org/10.1112/s0010437x15007629