On Ramanujan expansions with additive coefficients

Maurizio Laporta ()
Additional contact information
Maurizio Laporta: Università degli Studi di Napoli

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 2, 595-600

Abstract: Abstract The Ramanujan series attached to a complex-valued arithmetic function $$\widehat{g}$$ g ^ in a fixed integer a is the series $$\sum _n\widehat{g}(n)c_n(a)$$ ∑ n g ^ ( n ) c n ( a ) , where $$c_n(a)$$ c n ( a ) is the so-called Ramanujan sum. Assuming that $$\widehat{g}$$ g ^ is additive or, more generally, a product of a multiplicative function with an additive one, we study the relationships between the Ramanujan series attached to $$\widehat{g}$$ g ^ in a positive integer a and its subseries obtained by taking the terms with n coprime to a fixed integer $$d\ge 2$$ d ≥ 2 .

Keywords: Ramanujan expansion; Additive function; Multiplicative function; Series identity; Primary 11A25; Secondary 11N37; 11K65 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-023-00504-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:56:y:2025:i:2:d:10.1007_s13226-023-00504-0

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-023-00504-0

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().