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

B. Ramakrishnan, Brundaban Sahu, Anup Kumar Singh

If $f(z)$ is a modular form of weight $k$, then the differential operator ${\vartheta }_k$ defined by ${\vartheta }_k(f)=\frac{1}{2\pi i}\frac{d}{dz}f(z)-\frac{k}{12}{E}_2(z)f(z)$ (kno…