The average size of Ramanujan sums over quadratic number fields(II)

2021/09/23 by Wenguang Zhai, Zhai, Wenguang
Mathematics · #11M41 #11N37 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2109.11111

openalex publication_date 2021/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study Ramanujan sums c_{\bf m}(\bf n), where \bf m and \bf n are integral ideals in an arbitrary quadratic number field. We give some new results about the asymptotic behavior of sums of c_{\bf m}(\bf n) over both \bf m and \bf n.

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