Starts 30 May 2023 14:00
Ends 30 May 2023 15:00
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The variance of a general class of multiplicative functions in short intervals
ICTP (and Zoom)
Leonardo Building - Luigi Stasi Seminar Room
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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.
https://zoom.us/meeting/register/tJEpc-qrpjsrH9ZNpox8ieRFL_mKVul_NUTe
After registering, you will receive a confirmation email containing information about joining the meeting.
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.