Distribution of exponential functions with squarefull exponent in residue rings

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticle

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 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.

Original languageEnglish
Pages (from-to)283-289
Number of pages7
JournalIndagationes Mathematicae
Volume15
Issue number2
DOIs
Publication statusPublished - 21 Jun 2004

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