Number Theory seminar: Chiara Bellotti (UNSW Canberra)

Event Type: Lecture
Sponsor: Department of Mathematics
Virtual: Join online
Date: Apr 4, 2023 5:00 pm
Speaker: Chiara Bellotti
Contact: Kevin Ford
E-Mail: ford126@illinois.edu
Views: 27
Originating Calendar: Number Theory Seminar Calendar; On the generalised Dirichlet divisor problem

In this talk we present new unconditional estimates on $\Delta_k(x)$, the remainder term of the generalised divisor function, for large $k$. By combining new estimates of exponential sums and Carlson's exponent, we show that $\Delta_k(x) \ll x^{1 - 1.224(k - 8.37)^{-2/3}}$ for $k\ge 30$ and $\Delta_k(x) \ll x^{1 - 3.699k^{-2/3}}$ for all sufficiently large fixed $k$. This is a joint work with Andrew Yang.

Department of Mathematics - Master Calendar