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On the Number of Products Which Form Perfect Powers and Discriminants of Multiquadratic Extensions by de la Bretà̈che, Régis; Kurlberg, Pär; Shparlinski, Igor E is a Mathematics article available to read on EtoBox.

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Abstract We study some counting questions concerning products of positive integers $u_1, \ldots , u_n$, which form a nonzero 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 that are multiquadratic extensions of ${\mathbb{Q}}$ and improve and generalize a result of N. Rome (2017).

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Author

de la Bretà̈che, Régis; Kurlberg, Pär; Shparlinski, Igor E

Publisher

Oxford University Press; Oxford University Press (OUP) (ISSN 1073-7928)

Published

2019

Language

EN

Field

Mathematics (Physical Sciences)