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ON SOLUTIONS TO SOME POLYNOMIAL CONGRUENCES IN SMALL BOXES

  • IGOR E. SHPARLINSKI (a1)
Abstract

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.

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COPYRIGHT: ©2013 Australian Mathematical Publishing Association Inc. 
References
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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