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

  • Date: 10/06/2022
Pranendu DarbarNorwegian University of Science and Technology



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

Other Information: 

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.