Counting fundamental solutions to the Pell equation with prescribed size. (11th November 2018) - Xi, Ping
Abstract : The cardinality of the set of Dx for which the fundamental solution of the Pell equation t^2-Du^2=1 is less than D^1/2+[STIX]x1D6FC with [STIX]x1D6FC[12, 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.