The Average Size of Ramanujan Sums over Cubic Number Fields

2021/05/25 by Jing Ma, Ma, Jing, Huayan Sun +3
Mathematics · #11N37 11L03 11R16 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2105.11699

openalex publication_date 2021/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a cubic number field. In this paper, we study the Ramanujan sums c_J(I), where I and J are integral ideals in O_K. The asymptotic behaviour of sums of c_J(I) over both I and J is investigated.

Related

• The average size of Ramanujan sums over quadratic number fields(II)
• On the distribution of Ramanujan Sums over number fields
• Moments of Averages of Ramanujan Sums over Number Fields
• The ideal counting function in cubic fields
• On a generalization of arithmetic functions and the Ramanujan sums