On Cilleruelo's conjecture for the least common multiple of polynomial sequences

Zeév Rudnick, Sa'ar Zehavi

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

A conjecture due to Cilleruelo states that for an irreducible polynomial f with integer coefficients of degree d ≥ 2, the least common multiple Lf(N) of the sequence f(1), f(2),..., f(N) has asymptotic growth log Lf(N) ∼ (d − 1)N log N as N → ∞. We establish a version of this conjecture for almost all shifts of a fixed polynomial, the range of N depending on the range of shifts.

Original languageEnglish
Pages (from-to)1441-1458
Number of pages18
JournalRevista Matematica Iberoamericana
Volume37
Issue number4
DOIs
StatePublished - 1 Jan 2021
Externally publishedYes

Keywords

  • Irreducible polynomial
  • Least common multiple
  • Primes

ASJC Scopus subject areas

  • General Mathematics

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