Relation between Borweins’ Cubic Theta Functions and Ramanujan’s Eisenstein Series-Reference-Cited by-同舟云学术

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

Published:2021-05-08 Issue: Volume:2021 Page:1-6
ISSN:1687-0042
Container-title:Journal of Applied Mathematics
language:en
Short-container-title:Journal of Applied Mathematics

Author:

Kumar B. R. Srivatsa¹,Shruthi ¹,Radha D. Anu¹^ORCID

Affiliation:

1. Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576 104, India

Abstract

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.

Publisher

Hindawi Limited

Subject

Applied Mathematics

Link

http://downloads.hindawi.com/journals/jam/2021/6614572.pdf

Reference14 articles.

1. A cubic counterpart of Jacobi’s identity and the AGM;J. M. Borwein;Transactions of the American Mathematical Society,1991

2. Some cubic modular identities of Ramanujan

3. Ramanujan’s theories of elliptic functions to alternative bases;B. C. Berndt;Transactions of the American Mathematical Society,1995

4. On the two-dimensional theta functions of the Borweins

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