Average Size of Ramanujan Sum Associated with Divisor Function

Xin Li () and Wenguang Zhai
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Xin Li: Department of Mathematics, China University of Mining and Technology, Beijing 100083, China
Wenguang Zhai: Department of Mathematics, China University of Mining and Technology, Beijing 100083, China

Mathematics, 2025, vol. 13, issue 5, 1-16

Abstract: Let m and n be positive integers, and let c ( m , n ) denote the Ramanujan sum. In this paper, we establish an asymptotic formula for the mean value of c ( m , n ) , which is associated with the divisor function, over both m and n .

Keywords: Ramanujan sum; moment; divisor function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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