تقرير
The Chebotarev density theorem for function fields -- incomplete intervals
| العنوان: | The Chebotarev density theorem for function fields -- incomplete intervals |
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| المؤلفون: | Kurlberg, Pär, Rosenzweig, Lior |
| سنة النشر: | 2019 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11N05, 11T06 |
| الوصف: | We prove a Polya-Vinogradov type variation of the the Chebotarev density theorem for function fields over finite fields valid for "incomplete intervals" $I \subset \mathbb{F}_p$, provided $(p^{1/2}\log p)/|I| = o(1)$. Applications include density results for irreducible trinomials in $\mathbb{F}_p[x]$, i.e. the number of irreducible polynomials in the set $\{ f(x) = x^{d} + a_{1} x + a_{0} \in \mathbb{F}_p[x] \}_{a_{0} \in I_{0}, a_{1}\in I_{1}}$ is $\sim |I_{0}|\cdot |I_{1}|/d$ provided $|I_{0}| > p^{1/2+\epsilon}$, $|I_{1}| > p^{\epsilon}$, or $|I_{1}| > p^{1/2+\epsilon}$, $|I_{0}| > p^{\epsilon}$, and similarly when $x^{d}$ is replaced by any monic degree $d$ polynomial in $\mathbb{F}_p[x]$. Under the above assumptions we can also determine the distribution of factorization types, and find it to be consistent with the distribution of cycle types of permutations in the symmetric group $S_{d}$. Comment: Minor revision |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1901.06751 |
| رقم الأكسشن: | edsarx.1901.06751 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |