On Arithmetic Properties of Products and Shifted Products

Joël Rivat () and András Sárközy ()
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Joël Rivat: Université d’Aix-Marseille, Institut de Mathématiques de Marseille, CNRS UMR 7373
András Sárközy: Eötvös Loránd University, Department of Algebra and Number Theory

A chapter in Analytic Number Theory, 2015, pp 345-355 from Springer

Abstract: Abstract Let 𝒜 $$\mathcal{A}$$ and ℬ $$\mathcal{B}$$ be large subsets of { 1 … , N } $$\{1\ldots,N\}$$ . Arithmetic properties of the products ab, resp. of the shifted products ab + 1 with a ∈ 𝒜 $$a \in \mathcal{A}$$ , b ∈ ℬ $$b \in \mathcal{B}$$ are studied. In particular, it is shown that the sum of digits of the products ab is well distributed, and the size of the subsets 𝒜 , ℬ ∈ { 1 … , N } $$\mathcal{A},\mathcal{B}\in \{ 1\ldots,N\}$$ with the property that ab + 1 is always squarefree is estimated.

Keywords: Product of sequences; Shifted products; Digit properties; Squares; Multiplicative characters; Large sieve; Primary 11N25; Secondary 11K45; 11N36 (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-22240-0_21

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DOI: 10.1007/978-3-319-22240-0_21

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