Concentration of points on curves in finite fields

Javier Cilleruelo; Igor Shparlinski

doi:10.1007/s00605-013-0498-x

Concentration of points on curves in finite fields

Javier Cilleruelo, Igor Shparlinski^*

^*Corresponding author for this work

School of Computing

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

14 Citations (Scopus)

Abstract

We obtain analogues of several recent bounds on the number of solutions of polynomial congruences modulo a prime with variables in short intervals in the case of polynomial equations in high degree extensions of finite fields. In these settings low-dimensional affine spaces play the role of short intervals and thus several new ideas are required.

Original language	English
Pages (from-to)	315-327
Number of pages	13
Journal	Monatshefte fur Mathematik
Volume	171
Issue number	3-4
DOIs	https://doi.org/10.1007/s00605-013-0498-x
Publication status	Published - Sept 2013

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title = "Concentration of points on curves in finite fields",

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AU - Shparlinski, Igor

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AB - We obtain analogues of several recent bounds on the number of solutions of polynomial congruences modulo a prime with variables in short intervals in the case of polynomial equations in high degree extensions of finite fields. In these settings low-dimensional affine spaces play the role of short intervals and thus several new ideas are required.

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Concentration of points on curves in finite fields

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