The largest prime factor of an irreducible cubic polynomial
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908812659654656 |
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| author | Ermoshin, Ivan |
| author_facet | Ermoshin, Ivan |
| contents | Heath-Brown proved that for a positive proportion of integers $n$, $n^3+2$ has a prime factor larger than $n^{1+c}$ with $c=10^{-303}$.
We generalize this result to arbitrary monic irreducible cubic polynomial of $\mathbb{Z}[x]$ with $c$ replaced by an exponent $c_p$ dependent on the polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03642 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The largest prime factor of an irreducible cubic polynomial Ermoshin, Ivan Number Theory Heath-Brown proved that for a positive proportion of integers $n$, $n^3+2$ has a prime factor larger than $n^{1+c}$ with $c=10^{-303}$. We generalize this result to arbitrary monic irreducible cubic polynomial of $\mathbb{Z}[x]$ with $c$ replaced by an exponent $c_p$ dependent on the polynomial. |
| title | The largest prime factor of an irreducible cubic polynomial |
| topic | Number Theory |
| url | https://arxiv.org/abs/2602.03642 |