Resumen de On Cilleruelo’s conjecture for the least common multiple of polynomial sequences
Zeév Rudnick, Sa'ar Zehavi
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.
