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2 results

  • ON SOLUTIONS TO SOME POLYNOMIAL CONGRUENCES IN SMALL BOXES

  • Part of
  • IGOR E. SHPARLINSKI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 89 / Issue 2 / April 2014
    Published online by Cambridge University Press:
    07 August 2013, pp. 300-307
    Print publication:
    April 2014
    • Article
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  • We use bounds of mixed character sum to study the distribution of solutions to certain polynomial systems of congruences modulo a prime $p$. In particular, we obtain nontrivial results about the number of solutions in boxes with the side length below ${p}^{1/ 2} $, which seems to be the limit of more general methods based on the bounds of exponential sums along varieties.

  • APPROXIMATION BY SEVERAL RATIONALS

  • Part of
  • IGOR E. SHPARLINSKI
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 77 / Issue 2 / April 2008
    Published online by Cambridge University Press:
    01 April 2008, pp. 325-329
    Print publication:
    April 2008
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  • Following T. H. Chan, we consider the problem of approximation of a given rational fraction a/q by sums of several rational fractions a1/q1,…,an/qn with smaller denominators. We show that in the special cases of n=3 and n=4 and certain admissible ranges for the denominators q1,…,qn, one can improve a result of T. H. Chan by using a different approach.