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A lower bound on the least common multiple of polynomial sequences

Abstract:
For an irreducible polynomial f∈ℤ[x] of degree d≥2, Cilleruelo conjectured that the least common multiple of the values of the polynomial at the first N integers satisfies loglcm(f(1),…,f(N))∼(d−1)NlogN as N→∞. This is only known for degree d=2. We give a lower bound for all degrees d≥2 which is consistent with the conjecture: loglcm(f(1),…,f(N))≫NlogN.
Publication status:
Published
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Magdalen College
Role:
Author
ORCID:
0000-0001-5782-7082
Publisher:
University of Parma Publisher's website
Journal:
Rivista di Matematica della Università di Parma Journal website
Volume:
12
Issue:
1
Pages:
143-150
Publication date:
2021-01-01
Acceptance date:
2020-03-19
EISSN:
2284-2578
ISSN:
0035-6298
Language:
English
Keywords:
Pubs id:
1230570
Local pid:
pubs:1230570
Deposit date:
2022-01-14

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