Izvorni znanstveni članak

https://doi.org/10.3336/gm.44.1.02

On the distribution of solutions to linear equations

Igor Shparlinski ; Department of Computing, Macquarie University, Sydney, Australia

Sažetak

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.

Ključne riječi

Linear equations; uniform distribution; exponential sums

Hrčak ID:

36943

URI

https://hrcak.srce.hr/36943

Datum izdavanja:

21.5.2009.

Posjeta: 1.360 *