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arXiv · 1601.05180

On the divisibility of class numbers and discriminants of imaginary quadratic fields

Meng Fai Lim
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Abstract

Let $n$ be a squarefree positive odd integer. We will show that there exist infinitely many imaginary quadratic number fields with discriminant divisible by $n$ and-at the same time-having an element of order $n$ in the class group. We then apply our result to prove that for a given squarefree positive odd integer $n$ there exist infinitely many $N$ such that $n$ divides both $N$ and $r(N)$, where $r(N)$ is the representation number of $N$ as sums of three squares.

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Meng Fai Lim. 2016-01-20. On the divisibility of class numbers and discriminants of imaginary quadratic fields. https://arxiv.org/abs/1601.05180

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