On correlations of certain multiplicative functions
R. Balasubramanian, Sumit Giri, Priyamvad Srivastav

TL;DR
This paper investigates the asymptotic behavior of sums involving shifted products of multiplicative functions, providing new formulas and improved error estimates that are independent of the shift parameter.
Contribution
It derives asymptotic formulas for sums of shifted products of multiplicative functions, including cases with the Möbius squared function, with enhanced error bounds.
Findings
Asymptotic formulas for sums of shifted products of multiplicative functions.
Improved error terms that are independent of the shift parameter.
Extensions to sums involving the Möbius squared function.
Abstract
In this paper, we study sums of shifted products for any and arithmetic functions and , with and small. We obtain asymptotic formula for different orders of magnitude of and . We also provide asymptotic formula for sums of the type , where and is small. For small order of magnitudes of and , we improve the error terms and make them independent of .
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Taxonomy
TopicsAnalytic Number Theory Research · Coding theory and cryptography · Advanced Mathematical Identities
