Average Size of Ramanujan Sum Associated with Divisor Function

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.

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Journal
Mathematics
Published
2025-02-21
DOI
https://doi.org/10.3390/math13050697
Primary Topic
Analytic Number Theory Research
Type
article
Field-Weighted Citation Impact
0.00

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article

Average Size of Ramanujan Sum Associated with Divisor Function

Xin Li, Wenguang Zhai
Mathematics
Analytic Number Theory Research
article

Average Size of Ramanujan Sum Associated with Divisor Function

Xin Li, Wenguang Zhai
article en

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.

MathematicsVol. 13(5)
China University of Mining and Technology (CN)
National Natural Science Foundation of China
Openalex Percentile: Top 94%
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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Average Size of Ramanujan Sum Associated with Divisor Function — Xin Li, Wenguang Zhai · Mathematics (2025) | TGRS Research Map | TGRS