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- W2912179670 abstract "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 $S_{d}$." @default.
- W2912179670 created "2019-02-21" @default.
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- W2912179670 date "2019-01-20" @default.
- W2912179670 modified "2023-10-01" @default.
- W2912179670 title "The Chebotarev density theorem for function fields -- incomplete intervals" @default.
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