Sum of three squares and class numbers of imaginary quadratic fields. (English) Zbl 1256.11058

Cho, Peter Jaehyun

Proc. Japan Acad., Ser. A 87, No. 6, 91-94 (2011).

The author proves that, for given positive integers \(k\) and suitably chosen integers \(a\) and \(M\), there exist infinitely many positive squarefree integers \(d\) such that \(h(-d)\) is divisible by \(k\) with \(d \equiv a \bmod M\). Using a result of Gauss, this divisibility result is then transferred to the number of representations of integers as sums of three squares.

Reviewer: Franz Lemmermeyer (Jagstzell)

MSC:

11R11	Quadratic extensions
11R29	Class numbers, class groups, discriminants

Keywords:

complex quadratic number field; class number

References:

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