Some Eisenstein Series Identities Related to Modular Equations of the Seventh Order

@inproceedings{Liu2003SomeES,
  title={Some Eisenstein Series Identities Related to Modular Equations of the Seventh Order},
  author={Zhi-Guo Liu},
  year={2003}
}
In this paper we will use one well-known modular equation of seventh order, one theta function identity of S. McCullough and L.-C. Shen, 1994, and the complex variable theory of elliptic functions to prove some new septic identities for theta functions. Then we use these identities to provide new proofs of some Eisenstein series identities in Ramanujan’s notebooks or “lost” notebook. We also derive a new identity for Eisenstein series and some curious trigonometric identities. 

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 18 references

On the additive formula of the theta functions and a collection of Lambert series pertaining to the modular equations of degree 5

L.-C. Shen
Trans. Amer. Math. Soc., • 1994
View 8 Excerpts
Highly Influenced

A new class of theta-function identities originating in Ramanujan’s notebooks

B. C. Berndt, L.-C. Zhang
J. Number Theory, • 1994
View 3 Excerpts
Highly Influenced

Son, Eisenstein series in Ramanujan’s lost notebook

B. C. Berndt, H. H. Chan, S.H.J. Sohn
Ramanujan J., • 2000
View 1 Excerpt

The Borweins’ cubic theta function identity and some cubic modular identities of Ramanujan

Z.-G. Liu
Ramanujan J., • 2000
View 1 Excerpt

On the Szgö kernel of an annulus

S. McCullough, L.-C. Shen
Proc. Amer. Math. Soc., • 1994
View 1 Excerpt

Eisenstein series in Ramanujan ’ s lost notebook

B. C. Berndt, H. H. Chan, J. Sohn, S. H. Son
Ramanujan ’ s Notebooks , Part III • 1991

Ramanujan’s Notebooks, Part III, Springer-Verlag

B. C. Berndt
New York, • 1991

Rangachari, Ramanujan’s elliptic integrals and modular identities, in ‘Number Theory and Related Topics

S.S.S. Raghavan
MR 98b:11045, • 1989
View 1 Excerpt

The Lost Notebook and Other Unpublished Papers, Narosa

S. Ramanujan
New Delhi, • 1988

Similar Papers

Loading similar papers…