MATH Seminar

Title: On the number of small prime power residues
Seminar: Algebra
Speaker: Kubra Benli of University of Georgia
Contact: David Zureick-Brown,
Date: 2019-10-22 at 4:00PM
Venue: MSC W303
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Let $p$ be a prime number. For each positive integer $k\geq 2$, it is widely believed that the smallest prime that is a $k$th power residue modulo $p$ should be $O(p^{\epsilon})$, for any $\epsilon>0$. Elliott has proved that such a prime is at most $p^{\frac{k-1}{4}+\epsilon}$, for each $\epsilon>0$. In this talk we will discuss the distribution of the prime $k$th power residues modulo $p$ in the range $[1, p]$, with a more emphasis on the subrange $[1,p^{\frac{k-1}{4}+\epsilon}]$, for $\epsilon>0$.

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