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Level 20 Eisenstein series identities and their combinatorial properties

https://doi.org/10.26907/0021-3446-2025-9-25-37

Abstract

T. Huber, D. Schultz and D. Ye have obtained four Eisenstein series identities of level 20 and employed them to derive a new series for 1 \pi . Motivated by this, in this article, nine new Eisenstein series identities of level 20 are presented and their combinatorial properties are given. 

About the Authors

G. Vinay
Dr. Ambedkar Institute of Technology
India

G. Vinay

Bengaluru, 560056



. Siddaraju
Government First Grade College for Women
India

Siddaraju

Chamarajanagara, 571313



C.S. Shivakumar Swamy
Government College for Women (Autonomous)
India

C.S. Shivakumar Swamy

Mandya, 571401



References

1. Whittaker E.T., Watson G.N. A course of modern analysis (Cambridge Univ. Press, 1962).

2. Huber T., Schultz D., Ye D. "Series for 1/π of level 20", J. Number Theory 188, 121-136 (2018).

3. Anusha T. "An elementary approach to Eisenstein series identities of Huber, Schultz and Ye", Indian J. Pure Appl. Math. 50 (4), 971-978 (2019).

4. Berndt B.C. Ramanujan's notebook. P. III (Springer-Verlag, New York, 1991).

5. Berndt B.C. Ramanujan's Notebooks. II (Tata institute of fundamental Research, Bombay, 1957).

6. Gugg C. "Two modular equations for squares of the Rogers-Ramanujan functions with applications", Ramanujan J. 18, 183-207 (2009).

7. Bhuvan E.N. A Classical approach to Ramanujan's type Eisenstein series and incomplete elliptic integrals, Ph.D thesis (Univ. Mysore, 2008).

8. Berndt B.C. Ramanujan's notebooks. II (Springer-Verlag, New York, 1989).


Review

For citations:


Vinay G., Siddaraju , Shivakumar Swamy C. Level 20 Eisenstein series identities and their combinatorial properties. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2025;1(9):25-37. (In Russ.) https://doi.org/10.26907/0021-3446-2025-9-25-37

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