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Bilinear character sums and sum-product problems on elliptic curves

Part of: Arithmetic algebraic geometry

Published online by Cambridge University Press:  12 January 2010

Omran Ahmadi  and
Igor Shparlinski
Omran Ahmadi
Affiliation:
Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Igor Shparlinski
Affiliation:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia, Email: (igor@comp.mq.edu.au)
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Abstract

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Let E be an ordinary elliptic curve over a finite field q of q elements. We improve a bound on bilinear additive character sums over points on E, and obtain its analogue for bilinear multiplicative character sums. We apply these bounds to some variants of the sum-product problem on E.

Keywords

sum-product problemelliptic curvescharacter sums

MSC classification

Secondary: 11G05: Elliptic curves over global fields
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 1 , February 2010 , pp. 1 - 12
Copyright
Copyright © Edinburgh Mathematical Society 2010