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

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.


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