A lower bound on the least common multiple of polynomial sequences
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 con...
| Main Authors: | , |
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| פורמט: | Journal article |
| שפה: | English |
| יצא לאור: |
University of Parma
2021
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| _version_ | 1826270994030919680 |
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| author | Maynard, J Rudnick, Z |
| author_facet | Maynard, J Rudnick, Z |
| author_sort | Maynard, J |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T21:49:37Z |
| format | Journal article |
| id | oxford-uuid:4acb1f6d-6f45-4383-9b9f-82d433b543ac |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:49:37Z |
| publishDate | 2021 |
| publisher | University of Parma |
| record_format | dspace |
| spelling | oxford-uuid:4acb1f6d-6f45-4383-9b9f-82d433b543ac2022-03-26T15:39:43ZA lower bound on the least common multiple of polynomial sequencesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4acb1f6d-6f45-4383-9b9f-82d433b543acEnglishSymplectic ElementsUniversity of Parma2021Maynard, JRudnick, ZFor 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. |
| spellingShingle | Maynard, J Rudnick, Z A lower bound on the least common multiple of polynomial sequences |
| title | A lower bound on the least common multiple of polynomial sequences |
| title_full | A lower bound on the least common multiple of polynomial sequences |
| title_fullStr | A lower bound on the least common multiple of polynomial sequences |
| title_full_unstemmed | A lower bound on the least common multiple of polynomial sequences |
| title_short | A lower bound on the least common multiple of polynomial sequences |
| title_sort | lower bound on the least common multiple of polynomial sequences |
| work_keys_str_mv | AT maynardj alowerboundontheleastcommonmultipleofpolynomialsequences AT rudnickz alowerboundontheleastcommonmultipleofpolynomialsequences AT maynardj lowerboundontheleastcommonmultipleofpolynomialsequences AT rudnickz lowerboundontheleastcommonmultipleofpolynomialsequences |