Relation between Borweins’ Cubic Theta Functions and Ramanujan’s Eisenstein Series

B. R. Srivatsa Kumar; Shruthi; D. Anu Radha

doi:10.1155/2021/6614572

Journal of Applied Mathematics (Jan 2021)

Relation between Borweins’ Cubic Theta Functions and Ramanujan’s Eisenstein Series

B. R. Srivatsa Kumar,
Shruthi,
D. Anu Radha

Affiliations

B. R. Srivatsa Kumar: Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576 104, India
Shruthi: Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576 104, India
D. Anu Radha: Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576 104, India

DOI: https://doi.org/10.1155/2021/6614572
Journal volume & issue: Vol. 2021

Abstract

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Two-dimensional theta functions were found by the Borwein brothers to work on Gauss and Legendre’s arithmetic-geometric mean iteration. In this paper, some new Eisenstein series identities are obtained by using (p, k)-parametrization in terms of Borweins’ theta functions.

Published in Journal of Applied Mathematics

ISSN: 1110-757X (Print); 1687-0042 (Online)
Publisher: Wiley
Country of publisher: United Kingdom
LCC subjects: Science: Mathematics
Website: https://onlinelibrary.wiley.com/journal/4185

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