Ramanujan — Fourier series and a theorem of Ingham

H. Gopalakrishna Gadiyar (), M. Ram Murty () and R. Padma ()
Additional contact information
H. Gopalakrishna Gadiyar: VIT University
M. Ram Murty: Queen’s University
R. Padma: VIT University

Indian Journal of Pure and Applied Mathematics, 2014, vol. 45, issue 5, 691-706

Abstract: Abstract Given two arithmetical functions f, g, we derive, under suitable conditions, asymptotic formulas for the convolution sums ∑ n≤N f (n) g (n + h) for a fixed number h. To this end, we develop the theory of Ramanujan expansions for arithmetical functions. Our results give new proofs of some old results of Ingham proved by him in 1927 using different techniques.

Keywords: Ramanujan-Fourier series; Ramanujan sums; convolutions sums (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s13226-014-0084-5 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:45:y:2014:i:5:d:10.1007_s13226-014-0084-5

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

DOI: 10.1007/s13226-014-0084-5

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 ().