A Study of Twisted Sums of Arithmetic Functions

Speaker: Saloni Sinha

Date: Tue, Oct 15, 2024

Location: PIMS, University of British Columbia, Online, Zoom

Subject: Mathematics, Number Theory

Class: Scientific

CRG: L-Functions in Analytic Number Theory

Abstract:

We study sums of the form $\sum_{n\leq x} f(n) n^{-iy}$, where $f$ is an arithmetic function, and we establish an equivalence between the Riemann Hypothesis and estimates on these sums. In this talk, we will explore examples of such sums with specific arithmetic functions, as well as discuss potential implications and future research directions.