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

  • Zeév Rudnick

    Tel Aviv University, Israel
  • Sa'ar Zehavi

    Tel Aviv University, Israel
On Cilleruelo’s conjecture for the least common multiple of polynomial sequences cover

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Abstract

A conjecture due to Cilleruelo states that for an irreducible polynomial with integer coefficients of degree , the least common multiple of the sequence has asymptotic growth as . We establish a version of this conjecture for almost all shifts of a fixed polynomial, the range of depending on the range of shifts.

Cite this article

Zeév Rudnick, Sa'ar Zehavi, On Cilleruelo’s conjecture for the least common multiple of polynomial sequences. Rev. Mat. Iberoam. 37 (2021), no. 4, pp. 1441–1458

DOI 10.4171/RMI/1234