The variance of a general class of multiplicative functions in short intervals

Speaker: Mithun Das (National Institute of Science Education and Research (NISER), India)
Abstract: In this talk, we shall discuss a general class of multiplicative functions by relating "short averages" to its "long average". More precisely, we shall talk about estimating the variance of such a class of functions in short intervals asymptotically, using Fourier analysis and counting rational points on certain binary forms. Our result is applicable to the interesting multiplicative functions, namely, $k$-free numbers, Euler's totient function, generalized divisor function, and many others that establish various new results and improvements in short intervals to the literature. This is joint work with Pranendu Darbar.