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

• Zeév Rudnick ^[1] ; Sa'ar Zehavi ^[1]
  1. [1] Tel Aviv University

     Tel Aviv University

     Israel

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 4, 2021, págs. 1441-1458
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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 logLf(N)∼(d−1)NlogN 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.