Size of regulators and consecutive square-free numbers

作者：Fouvry Etienne^*; Jouve Florent

来源：Mathematische Zeitschrift, 2013, 273(3-4): 869-882.

DOI：10.1007/s00209-012-1035-7

We prove that, for almost all D, the fundamental solution of the associated Pell equation x (2)-Dy (2) = 1 is greater than D (1.749 center dot center dot center dot). We also show a strong link between this question and the error term in the asymptotic formula of the number of pairs of consecutive square-free numbers.

• 出版日期2013-4