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Weil Sums over Small Subgroups

Part of: Exponential sums and character sums Diophantine equations Finite fields and commutative rings (number-theoretic aspects)

Published online by Cambridge University Press:  15 August 2023

ALINA OSTAFE ,
IGOR E. SHPARLINSKI  and
JOSÉ FELIPE VOLOCH
ALINA OSTAFE
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia. e-mails: alina.ostafe@unsw.edu.au, igor.shparlinski@unsw.edu.au
IGOR E. SHPARLINSKI
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia. e-mails: alina.ostafe@unsw.edu.au, igor.shparlinski@unsw.edu.au
JOSÉ FELIPE VOLOCH
Affiliation:
School of Mathematics and Statistics, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand. e-mail: felipe.voloch@canterbury.ac.nz
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Abstract

We obtain new bounds on short Weil sums over small multiplicative subgroups of prime finite fields which remain nontrivial in the range the classical Weil bound is already trivial. The method we use is a blend of techniques coming from algebraic geometry and additive combinatorics.

MSC classification

Primary: 11T23: Exponential sums
Secondary: 11D79: Congruences in many variables 11L07: Estimates on exponential sums
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 176 , Issue 1 , January 2024 , pp. 39 - 53
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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