A Note on the Negative Pell Equation

Valentin Blomer ()
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Valentin Blomer: Universität Göttingen

A chapter in From Arithmetic to Zeta-Functions, 2016, pp 31-40 from Springer

Abstract: Abstract Nagell conjectured in the 1930s that the set of discriminants for which the negative Pell equation has an integral solution has an explicitly given positive proportion within the set of discriminants having no prime factor congruent to 3 modulo 4. In a series of papers, Fouvry and Klüners succeeded in showing that the order of magnitude of such discriminants up to x is indeed x(logx)−1∕2. Here we present a short independent argument that the order of magnitude is at least x(logx)−0. 62.

Keywords: Fundamental unit; Negative norm; Number of discriminants; Pell equation; Primary 11N45; Secondary 11D09 (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-28203-9_2

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DOI: 10.1007/978-3-319-28203-9_2

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