On the moments of averages of Ramanujan sums

2024/01/14 by Goel, Shivani, Murty, M. Ram
#11A05 #11L03 #11N37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2401.07321

Abstract

Chan and Kumchev studied averages of the first and second moments of Ramanujan sums. In this article, we extend this investigation by estimating the higher moments of averages of Ramanujan sums using the Brèteche Tauberian theorem. We also give a result for the moments of averages of Cohen-Ramanujan sums.

Related

• Moments of Averages of Ramanujan Sums over Number Fields
• On the distribution of Ramanujan Sums over number fields
• The second moment of Ramanujan sums
• On near orthogonality of certain k-vectors involving generalized Ramanujan sums
• The average size of Ramanujan sums over quadratic number fields(II)