On solutions to some polynomial congruences in small boxes

Igor E. Shparlinski

doi:10.1017/S0004972713000671

On solutions to some polynomial congruences in small boxes

Igor E. Shparlinski^*

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

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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.

Original language	English
Pages (from-to)	300-307
Number of pages	8
Journal	Bulletin of the Australian Mathematical Society
Volume	89
Issue number	2
DOIs	https://doi.org/10.1017/S0004972713000671
Publication status	Published - Apr 2014

Bibliographical note

Copyright the Publisher 2013. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

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10.1017/S0004972713000671

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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 p1/2, which seems to be the limit of more general methods based on the bounds of exponential sums along varieties.",

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AB - 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 p1/2, which seems to be the limit of more general methods based on the bounds of exponential sums along varieties.

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UR - http://purl.org/au-research/grants/arc/DP130100237

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On solutions to some polynomial congruences in small boxes

Abstract

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