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Title: On the distribution of solutions to linear equations
Related: Glasnik matematički, Vol. 44, No. 1, (2009), p.7-10
DOI: 10.3336/gm.44.1.02
Publisher: Hrvatsko Matematicko Drustvo
Date: 2009
FoR/RFCD Code(s): 010100 Pure Mathematics
Author/Creator: Shparlinski, Igor E
Description: Given two relatively prime positive integers m < n we consider the smallest positive solution (x0, y0) to the equation mx - ny = 1. E. I. Dinaburg and Y. G. Sinai have used continued fractions to show that the ratios x0/n are uniformly distributed in [0,1], when n and m run through consequtive integers of intervals of comparable sizes. We use a bound of exponential sums due to W. Duke, J. B. Friedlander and H. Iwaniec to show a similar result when m and n run through arbitrary sets which are not too thin.
Description: 4 page(s)
Subject Keyword: 010100 Pure Mathematics
Subject Keyword: linear equations
Subject Keyword: uniform distribution
Subject Keyword: exponential sums
Resource Type: journal article
Organisation: Macquarie University. Dept. of Computing

Macquarie University ResearchOnline