The Chowla–Selberg formula for abelian CM fields and Faltings heights Academic Article uri icon


  • © 2015 The Author. 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 τ and an analogous function τ2 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.

author list (cited authors)

  • Barquero-Sanchez, A., & Masri, R.

citation count

  • 1

publication date

  • September 2015