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{\Large Department of Mathematics, BGU}

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{\Huge AGNT}\\[0.2\baselineskip]

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\textbf{On} \emph{Wednesday, November  6, 2019}
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\textbf{At} \emph{15:10 -- 16:25}
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\textbf{In} \emph{-101}

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{\large\scshape Alexei Entin 
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  (TAU)
}
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will talk about
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{\Large\bfseries Factorization statistics for restricted polynomial specializations over large finite fields\par}
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\textsc{Abstract:}
For a polynomial $F(t,A_1,...,A_n)$ in $\mathbb{F}_p[t,A_1,...,A_n]$ ($p$ being a prime number) we study the factorization statistics of its specializations $F(t,a_1,...,a_n)$ in $\mathbb{F}_p[t]$ with $(a_1,...,a_n) \in S$, where $S=I_1\times\dots\times I_n\subset\mathbb{F}_{p^n}$ is a box, in the limit $p\rightarrow\infty$ and $deg(F)$ fixed. We show that under certain fairly general assumptions on $F$, and assuming that the box dimensions grow to infinity with one of them growing faster than $p^{1/2}$, the degrees of the irreducible factors of $F(t,a_1, \dots,a_n)$ are distributed like the cycle lengths of a random permutation in $S_n$.

This improves and generalizes previous results of Shparlinski and more recent results of Kurlberg-Rosenzweig, which in turn generalize the classical Polya-Vinogradov estimate of the number of quadratic residues in an interval.





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{\bfseries Please Note the Unusual Time!}
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