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 - 2021

Funding

FundersFunder number
Horizon 2020 Framework Programme786758

    Keywords

    • Irreducible polynomial
    • Least common multiple
    • Primes

    Fingerprint

    Dive into the research topics of 'On Cilleruelo's conjecture for the least common multiple of polynomial sequences'. Together they form a unique fingerprint.

    Cite this