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arXiv · 1902.01102

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

Zeév Rudnick·Sa'ar Zehavi
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Abstract

A conjecture due to Cilleruelo states that for an irreducible polynomial $f$ with integer coefficients of degree $d\geq 2$, the least common multiple $L_f(N)$ of the sequence $f(1), f(2), \dots, f(N)$ has asymptotic growth $\log L_f(N)\sim (d-1)N\log N$ as $N\to \infty$. 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.

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Zeév Rudnick, Sa'ar Zehavi. 2019-02-04. On Cilleruelo's conjecture for the least common multiple of polynomial sequences. https://arxiv.org/abs/1902.01102

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