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Published in:
2016 | OriginalPaper | Chapter
A Note on the Negative Pell Equation
Author : Valentin Blomer
Published in: From Arithmetic to Zeta-Functions
Publisher: Springer International Publishing
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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.