Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Dual Ramanujan-Fourier series
View through CrossRef
Let cq(n) be the Ramanujan sums. Many results concerning Ramanujan-Fourier series f (n) = ∞ q=1 aqcq(n) are obtained by many mathematicians. In this paper we study series of the form f (q) = ∞ n=1 ancq(n), which we call dual Ramanujan-Fourier series. We extend Lucht's theorem and Delange's theorem to this case and obtain some results.
Centre pour la Communication Scientifique Directe (CCSD)
Title: Dual Ramanujan-Fourier series
Description:
Let cq(n) be the Ramanujan sums.
Many results concerning Ramanujan-Fourier series f (n) = ∞ q=1 aqcq(n) are obtained by many mathematicians.
In this paper we study series of the form f (q) = ∞ n=1 ancq(n), which we call dual Ramanujan-Fourier series.
We extend Lucht's theorem and Delange's theorem to this case and obtain some results.
Related Results
New and explicit constructions of unbalanced Ramanujan bipartite graphs
New and explicit constructions of unbalanced Ramanujan bipartite graphs
AbstractThe objectives of this article are threefold. Firstly, we present for the first time explicit constructions of an infinite family of unbalanced Ramanujan bigraphs. Secondly...
Small diameters and generators for arithmetic lattices in $$\textrm{SL}_2(\mathbb {R})$$ and certain Ramanujan graphs
Small diameters and generators for arithmetic lattices in $$\textrm{SL}_2(\mathbb {R})$$ and certain Ramanujan graphs
AbstractWe show that arithmetic lattices in $$\textrm{SL}_{2}(\mathbb {R})$$
SL
2
...
Design and analysis of dual-curing systems
Design and analysis of dual-curing systems
Dual-curing processing is a method to prepare thermoset materials through two polymerization reactions carried out
simultaneously or sequentially. In these processes, a firm under...
On an identity of Ramanujan
On an identity of Ramanujan
Proofs published so far in articles and books, of the Ramanujan identity presented in this note, which depend on Euler products, are essentially the same as Ramanujan's original pr...
A note on the zeros of approximations of the Ramanujan $$\Xi $$-function
A note on the zeros of approximations of the Ramanujan $$\Xi $$-function
AbstractIn this paper we review the study of the distribution of the zeros of certain approximations for the Ramanujan $$\Xi $$
Ξ
-function given ...
Ramanujan Summation for Pascal’s Triangle
Ramanujan Summation for Pascal’s Triangle
The concept of Pascal’s triangle has fascinated not only professional mathematicians but also everyone interested in exploring science. Similarly, the idea of Ramanujan summation h...
Some New Ramanujan's Modular Equations of Degree 15
Some New Ramanujan's Modular Equations of Degree 15
Abstract
Ramanujan in his notebook recorded two modular equations involving multiplier with moduli of degrees (1,7) and (1,23). In this paper, we find some new Ramanujan's ...
A.K. Ramanujan: A Poet of Different Cultures and Languages
A.K. Ramanujan: A Poet of Different Cultures and Languages
The paper explores the impact of different cultures and languages in the poetic writings of A. K. Ramanujan. He has a full command over Indian culture, scriptures and rituals. Tami...