On a generalization of arithmetic functions and the Ramanujan sums

2012/12/09 by Yusuke Fujisawa, Fujisawa, Yusuke · 1 citation
Mathematics · Physics and Astronomy · #11A25 #11L26 #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A25 #msc:11L26

paper · pdf · doi:10.48550/arxiv.1212.1864

This paper has been withdrawn. The author noticed that this paper was not good

openalex publication_date 2012/12/09 · arxiv created 2014/04/27 · arxiv updated 2014/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a number field. This paper considers arithmetic functions over K, that are, complex valued functions on the set of nonzero integral ideals in K. Firstly we generalize some basic results on arithmetic functions. Next we define the generalized Ramanujan sums over K and show some properties.

Cited by

• On partial sums of the Möbius and Liouville functions for number fields

Related

• On sums of generalized Ramanujan sums
• On the distribution of Ramanujan Sums over number fields
• Ramanujan expansions of arithmetic functions of several variables over \mathbbF_q[T]
• Generalisations of Ramanujan sums for Polynomial rings over finite fields
• The average size of Ramanujan sums over quadratic number fields(II)