Utilization of Ramanujan-type Eisenstein series in the generation of differential equations

H. C. Vidya; B. A. Rao; H. C. Vidya; B. A. Rao

doi:10.3934/math.20241405

AIMS Mathematics

2024, Volume 9, Issue 10: 28955-28969. doi: 10.3934/math.20241405

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Research article

Utilization of Ramanujan-type Eisenstein series in the generation of differential equations

H. C. Vidya ¹,
B. A. Rao ^{2
,
,}

1.
Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576104, Karnataka, India
2.
Computer Science and Engineering Department, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576104, Karnataka, India

Received: 06 July 2024 Revised: 06 September 2024 Accepted: 12 September 2024 Published: 14 October 2024
MSC : 11F20, 11M36, 34K60

In his lost notebook, Ramanujan presented unique categories of remarkable infinite series, known as the Ramanujan-type Eisenstein series. The objective of this paper is to generate various differential identities related to classical $ \eta $-functions and $ h $-functions with the help of the Ramanujan-type Eisenstein series. Moreover, we present particular identities that incorporate Eisenstein series of different levels and $ h $-functions, thereby establishing links between class one infinite series and $ h $-functions.
- Eisenstein series,
- Dedekind $ \eta $-function,
- class one infinite series,
- differential equations
Citation: H. C. Vidya, B. A. Rao. Utilization of Ramanujan-type Eisenstein series in the generation of differential equations[J]. AIMS Mathematics, 2024, 9(10): 28955-28969. doi: 10.3934/math.20241405

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Abstract

In his lost notebook, Ramanujan presented unique categories of remarkable infinite series, known as the Ramanujan-type Eisenstein series. The objective of this paper is to generate various differential identities related to classical $ \eta $-functions and $ h $-functions with the help of the Ramanujan-type Eisenstein series. Moreover, we present particular identities that incorporate Eisenstein series of different levels and $ h $-functions, thereby establishing links between class one infinite series and $ h $-functions.

References

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