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

2019/02/04 by Zeév Rudnick, Rudnick, Zeév, Sa’ar Zehavi +1
Mathematics · #11N37 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Mathematical Dynamics and Fractals #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1902.01102

openalex publication_date 2019/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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