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 log lcm(f(1),..., f(N)) ~ (d - 1)N log N 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: log lcm(f(1),..., f(N)) » N log N.
| Original language | English |
|---|---|
| Pages (from-to) | 143-150 |
| Number of pages | 8 |
| Journal | Rivista di Matematica della Universita di Parma |
| Volume | 12 |
| Issue number | 1 |
| State | Published - 2021 |
Keywords
- Chebotarev density Theorem
- Prime factor
- polynomial
All Science Journal Classification (ASJC) codes
- General Mathematics