Kübra Benli

Deuring-Heilbronnn phenomenon, quantitatively established by Linnik in 1944, describes how the existence of a Landau-Siegel zero, which is real and near s=1, affects the location of the rest of the zeros of the Dirichlet L-functions to the same...

TBA

Let s(n) denote the sum of proper divisors of a positive integer n. In 1992, Erd\H{o}s, Granville, Pomerance, and Spiro conjectured that if  is a set of integers with asymptotic density zero then the preimage set s−1() also has asymptotic density...

In 1992, Erd˝os, Granville, Pomerance, and Spiro conjectured that if A is a set of integers with asymptotic density zero then the preimage of A under s(n), sum-of-proper-divisors function, also has asymptotic density zero. In this talk, we will...

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...

We improve the best known to date result of Dress-Iwaniec-Tenenbaum, getting (log x)^2 instead of (log x)^(5/2). We use a weighted form of Vaughan's identity, allowing a smooth truncation inside the procedure, and an estimate due to Barban-Vehov and...

We compute extreme values of the Riemann Zeta function at the critical points of the zeta function in the critical strip. i.e. the points where ζ′(s)=0 and Rs1. We show that the values taken by the zeta function at these points are very similar to...