ALMOST ALL PRIMES HAVE A MULTIPLE OF SMALL HAMMING WEIGHT

CHRISTIAN ELSHOLTZ*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

We improve recent results of Bourgain and Shparlinski to show that, for almost all primes (Formula presented.), there is a multiple (Formula presented.) that can be written in binary as (Formula presented.) with (Formula presented.) (corresponding to Hamming weight seven). We also prove that there are infinitely many primes (Formula presented.) with a multiplicative subgroup (Formula presented.), for some (Formula presented.), of size (Formula presented.), where the sum–product set (Formula presented.) does not cover (Formula presented.) completely.

Original languageEnglish
Pages (from-to)224-235
Number of pages12
JournalBulletin of the Australian Mathematical Society
Volume94
Issue number2
DOIs
Publication statusPublished - 23 May 2016

Keywords

  • additive bases
  • distribution of integers with multiplicative constraints
  • primes
  • sumsets
  • Waring’s problem and variants

ASJC Scopus subject areas

  • Mathematics(all)

Fields of Expertise

  • Information, Communication & Computing

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