## PIMS CRG Seminar Series: L-functions in Analytic Number Theory: Pranendu Darbar

- Date: 10/06/2022

Hybrid

Multiplicative functions in short intervals [video]

In this talk, we are interested in a general class of multiplicative functions. For a function that belongs to this class, we will relate its “short average” to its “long average”. More precisely, we will compute the variance of such a function over short intervals by using Fourier analysis and by counting rational points on certain binary forms. The discussion is applicable to some interesting multiplicative functions such as

$$

\mu_k(n), \frac{\phi (n)}{n}, \frac{n}{\phi (n)}, \mu^2(n)\frac{\phi(n)}{n},

\sigma_\alpha (n), (-1)^{\#\left\{p: p^k | n \right\}}

$$

and many others and it provides various new results and improvements to the previous result

in the literature. This is a joint work with Mithun Kumar Das.

This event is part of the PIMS CRG Group on *L*-Functions in Analytic Number Theory. More details can be found on the webpage here: https://sites.google.com/view/crgl-functions/crg-weekly-seminar

Kübra Benli, *Institut Élie Cartan de Lorraine
*

Fatma Çiçek, *University of Northern British Columbia
*

Ertan Elma, *University of Lethbridge*

The online seminars for the PIMS CRG L-functions in Analytic Number Theory will take place on **Thursdays, 10–11 am Pacific Time/11 am–noon Mountain Time**.

If you would like to attend the seminars, please register to receive the Zoom link.

You are also welcome to join us in person at our **“watch parties”**:

__UBC–Vancouver__: room ESB 4127

__University of Lethbridge__: M1060 (Markin Hall)

__University of Northern British Columbia__: 1084 Charles J McCaffray Hall

This event took place via zoom. A recording is available on mathtube.org.