Multiplicative functions in short intervals
Pranendu Darbar (The Norwegian University of Science and Technology)
Abstract: 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 \[ \mu_k(n), \, \, \frac{\phi(n)}{n}, \, \, \frac{n}{\phi(n)}, \, \, \mu^2(n)\frac{\phi(n)}{n}, \,\, \sigma_{\alpha}(n), \,\, (-1)^{\#\{p\,: \, p^k|n\}}(n), \] 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.
Mathematics
Audience: researchers in the topic
Series comments: These seminars will be centered on various topics in L-functions in analytic number theory. If you are interested, please register here to receive the Zoom link: uleth.zoom.us/meeting/register/tJ0ucO-spjkvEtGdqQv0rwzSYNjWjYBohVTu
| Organizers: | Fatma Çiçek*, Ertan Elma, Kubra Benli |
| *contact for this listing |