Year: 2018
Type: article
Abstract: The cardinality of the set of $D\leqslant x$ for which the fundamental solution of the Pell equation $t^{2}-Du^{2}=1$ is less than $D^{1/2+\unicode[STIX]{x1D6FC}}$ with $\unicode[STIX]{x1D6FC}\in [\frac{1}{2},1]$ is studied and certain lower bounds are obtained, improving previous results of Fouvry by introducing the $q$ -analogue of van der Corput method to algebraic exponential sums with smooth moduli.
Source: Compositio Mathematica
Author: Ping Xi
Institution: Xi'an Jiaotong University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Awards: G1448137079, G462502100
OpenAlex ID: W2606209159