The Variance of a General Class of Multiplicative Functions in Short Intervals

Explore the variance of multiplicative functions in short intervals through this advanced mathematics lecture. Delve into the asymptotic estimation of variance for a general class of multiplicative functions, utilizing Fourier analysis and rational point counting on binary forms. Discover how this approach applies to key multiplicative functions such as k-free numbers, Euler's totient function, and generalized divisor functions. Gain insights into new results and improvements in short interval analysis, presented by Mithun Das from the National Institute of Science Education and Research (NISER), India, in collaboration with Pranendu Darbar.

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