## 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.

### MSC:

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

### Keywords:

complex quadratic number field; class number
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### References:

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