## The PIMS Postdoctoral Fellow Seminar: Kübra Benli

- Date: 02/23/2022
- Time: 09:30

Online

Small prime $k$th power residues modulo $p$}

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 proved that such a prime is at most $p^{\frac{k-1}{4}+\epsilon}$, for each $\epsilon>0$. In this talk, we discuss the number of prime $k$th power residues modulo $p$ in the interval $[1,p^{\frac{k-1}{4}+\epsilon}]$ for $\epsilon>0$.

**Speaker Biography**: Kübra Benli received her B.S and M.S. degrees at Bogazici University in Istanbul, her M.S. supervisor was Prof. Cem Yalcin Yildirim. She then received her Ph.D. at the University of Georgia under the supervision of Prof. Paul Pollack in 2020. Since May 2021, she has been a postdoctoral fellow at the Institute Elie Cartan de Lorraine in Nancy, France working under the project ARITHRAND. She will begin her PIMS postdoctoral fellow at the University of Lethbridge later in 2022. Her research is on analytic/elementary number theory, with recent work focusing on counting primes in certain settings. She has also been working on some combinatorial problems. Her master thesis was published as a joint work and she has four publications, three of which are single authored as a result of her Ph.D. research.

This event is part of the Emergent Research: The PIMS Postdoctoral Fellow Colloquium Series.

This seminar takes places across multiple time zones: 9:30 AM Pacific/ 10:30 AM Mountain / 11:30 AM Central

**Register via Zoom** to receive the link for this event and the rest of the series.