On arithmetic properties of products and shifted products

Joël Rivat, András Sárközy

Research output: Chapter in Book/Report/Conference proceedingChapter

4 Citations (Scopus)

Abstract

Let A and B be large subsets of {1 …, N}. Arithmetic properties of the products ab+1, resp. of the shifted products ab C 1 with a ε A, b ε 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 ε {1 …, N} with the property that ab + 1 is always squarefree is estimated.

Original languageEnglish
Title of host publicationAnalytic Number Theory
Subtitle of host publicationIn Honor of Helmut Maier's 60th Birthday
PublisherSpringer International Publishing
Pages345-355
Number of pages11
ISBN (Electronic)9783319222400
ISBN (Print)9783319222394
DOIs
Publication statusPublished - Jan 1 2015

Keywords

  • Digit properties
  • Large sieve
  • Multiplicative characters
  • Product of sequences
  • Shifted products
  • Squares

ASJC Scopus subject areas

  • Mathematics(all)
  • Computer Science(all)

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    Rivat, J., & Sárközy, A. (2015). On arithmetic properties of products and shifted products. In Analytic Number Theory: In Honor of Helmut Maier's 60th Birthday (pp. 345-355). Springer International Publishing. https://doi.org/10.1007/978-3-319-22240-0_21