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arXiv · 1901.10694

On the number of products which form perfect powers and discriminants of multiquadratic extensions

Régis de la Bretèche·Pär Kurlberg·Igor E. Shparlinski
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Abstract

We study some counting questions concerning products of positive integers $u_1, \ldots, u_n$ which form a non-zero perfect square, or more generally, a perfect $k$-th power. We obtain an asymptotic formula for the number of such integers of bounded size and in particular improve and generalize a result of D. I. Tolev (2011). We also use similar ideas to count the discriminants of number fields which are multiquadratic extensions of $\mathbb{Q}$ and improve and generalize a result of N. Rome (2017).

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Régis de la Bretèche, Pär Kurlberg, Igor E. Shparlinski. 2019-11-19. On the number of products which form perfect powers and discriminants of multiquadratic extensions. https://arxiv.org/abs/1901.10694

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