Distribution of exponential functions with squarefull exponent in residue rings

Igor E. Shparlinski

doi:10.1016/S0019-3577(04)90020-1

Distribution of exponential functions with squarefull exponent in residue rings

Igor E. Shparlinski^*

^*Corresponding author for this work

School of Computing

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

4 Citations (Scopus)

Abstract

For a real x ≥ 1 we denote by S[x] the set of squarefull integers n ≤x, that is, the set of positive integers n ≤ such that l² n for any prime divisor l n. We estimate exponential sums of the form T_a (m,x) ∑n∈S[x] exp(2πia vⁿ/m) where ν is a fixed integer with gcd(ν,m) = 1, and apply them to studying the distribution of the powers νⁿ, n ε S[x], in the residue ring modulo m ≥ 1.

Original language	English
Pages (from-to)	283-289
Number of pages	7
Journal	Indagationes Mathematicae
Volume	15
Issue number	2
DOIs	https://doi.org/10.1016/S0019-3577(04)90020-1
Publication status	Published - 21 Jun 2004

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abstract = "For a real x ≥ 1 we denote by S[x] the set of squarefull integers n ≤x, that is, the set of positive integers n ≤ such that l2 n for any prime divisor l n. We estimate exponential sums of the form Ta (m,x) ∑n∈S[x] exp(2πia vn/m) where ν is a fixed integer with gcd(ν,m) = 1, and apply them to studying the distribution of the powers νn, n ε S[x], in the residue ring modulo m ≥ 1.",

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AB - For a real x ≥ 1 we denote by S[x] the set of squarefull integers n ≤x, that is, the set of positive integers n ≤ such that l2 n for any prime divisor l n. We estimate exponential sums of the form Ta (m,x) ∑n∈S[x] exp(2πia vn/m) where ν is a fixed integer with gcd(ν,m) = 1, and apply them to studying the distribution of the powers νn, n ε S[x], in the residue ring modulo m ≥ 1.

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IS - 2

ER -

Distribution of exponential functions with squarefull exponent in residue rings

Abstract

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