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

Huard, James G.; Kaplan, Pierre; Williams, Kenneth S.

Acta Arith. 73, No. 3, 271-301 (1995).

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)

MSC:

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

Keywords:

Chowla-Selberg formula for genera; class number; gamma function; binary quadratic forms with arbitrary discriminants

Citations:

Zbl 0166.05204