A random polynomial with multiplicative coefficients is almost surely irreducible
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909890021163008 |
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| author | Varjú, Péter P. Xu, Max Wenqiang |
| author_facet | Varjú, Péter P. Xu, Max Wenqiang |
| contents | Assume that the Riemann hypothesis holds for Dedekind zeta functions. Under this assumption, we prove that a degree $d$ polynomial with random multiplicative $\pm1$ coefficients is irreducible in $\mathbb{Z}[x]$ with probability $1-O(d^{-1/2+\varepsilon})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04240 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A random polynomial with multiplicative coefficients is almost surely irreducible Varjú, Péter P. Xu, Max Wenqiang Number Theory Combinatorics Probability Assume that the Riemann hypothesis holds for Dedekind zeta functions. Under this assumption, we prove that a degree $d$ polynomial with random multiplicative $\pm1$ coefficients is irreducible in $\mathbb{Z}[x]$ with probability $1-O(d^{-1/2+\varepsilon})$. |
| title | A random polynomial with multiplicative coefficients is almost surely irreducible |
| topic | Number Theory Combinatorics Probability |
| url | https://arxiv.org/abs/2511.04240 |