The Chowla-Selberg formula for genera. (English) Zbl 0855.11018

In 1967, S. Chowla and A. Selberg developed a now famous formula which bears their names. This formula is too complicated to state here, but it may be found in Crelle’s journal as formula 2, on page 110 of Epstein’s zeta function [J. Reine Angew. Math. 227, 86-110 (1967; Zbl 0166.05204)]. This formula holds for fundamental discriminants of quadratic fields. Others have extended the formula to arbitrary discriminants. Also, in 1993, K. S. Williams and N. Y. Zhang extended the Chowla-Selberg formula to genera of binary quadratic forms with underlying positive fundamental discriminant. In the paper under review, the authors extend the formula for genera to arbitrary discriminants.
Reviewer: R.Mollin (Calgary)


11E41 Class numbers of quadratic and Hermitian forms
11R42 Zeta functions and \(L\)-functions of number fields
11R11 Quadratic extensions
11E12 Quadratic forms over global rings and fields


Zbl 0166.05204
Full Text: DOI EuDML