On the exponential sum-product problem

Igor Shparlinski

doi:10.1016/S0019-3577(08)80006-7

On the exponential sum-product problem

Igor Shparlinski^*

^*Corresponding author for this work

School of Computing

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

4 Citations (Scopus)

Abstract

Let g be an element of order T over a finite field F_p of p elements, where p is a prime. We show that for a very wide class of sets A, B ∈ {1, . . ., T} at least one of the sets {g^{a b} : a ∈ A, b ∈ B} and {g^a + g^b : a ∈ A, b ∈ B} is large.

Original language	English
Pages (from-to)	325-331
Number of pages	7
Journal	Indagationes Mathematicae
Volume	19
Issue number	2
DOIs	https://doi.org/10.1016/S0019-3577(08)80006-7
Publication status	Published - Jun 2008

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title = "On the exponential sum-product problem",

abstract = "Let g be an element of order T over a finite field Fp of p elements, where p is a prime. We show that for a very wide class of sets A, B ∈ \{1, . . ., T\} at least one of the sets \{ga b : a ∈ A, b ∈ B\} and \{ga + gb : a ∈ A, b ∈ B\} is large.",

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AB - Let g be an element of order T over a finite field Fp of p elements, where p is a prime. We show that for a very wide class of sets A, B ∈ {1, . . ., T} at least one of the sets {ga b : a ∈ A, b ∈ B} and {ga + gb : a ∈ A, b ∈ B} is large.

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U2 - 10.1016/S0019-3577(08)80006-7

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JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

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ER -

On the exponential sum-product problem

Abstract

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