A simple extension of Ramanujan–Serre derivative map and some applications

Authors

B. Ramakrishnan, Indian Statistical Institute, Kolkata
Brundaban Sahu, Homi Bhabha National Institute
Anup Kumar Singh, Homi Bhabha National Institute

Article Type

Research Article

Publication Title

Ramanujan Journal

Abstract

If f(z) is a modular form of weight k, then the differential operator ϑk defined by ϑk(f)=12πiddzf(z)-k12E2(z)f(z) (known as the Ramanujan–Serre derivative map) is a modular form of weight k+ 2. In this paper, we obtain a simple extension of this map and use it to get a general method to derive certain convolution sums of the divisor functions (using the theory of modular forms). Explicit expressions are given for four types of convolution sums and we provide many examples for all these types of sums.

First Page

1379

Last Page

1410

DOI

https://10.1007/s11139-023-00704-6

Publication Date

8-1-2023

Recommended Citation

Ramakrishnan, B.; Sahu, Brundaban; and Singh, Anup Kumar, "A simple extension of Ramanujan–Serre derivative map and some applications" (2023). Journal Articles. 3636.
https://digitalcommons.isical.ac.in/journal-articles/3636