Rankin’s Method and Jacobi Forms of Several Variables B. Ramakrishnan and Brundaban Sahu

There are many interesting connections between differential operators and the theory of modular forms and many interesting results have been studied. In [10], R. A. Rankin gave a general description of the differential operators which send modular forms to modular forms. In [6], H. Cohen constructed bilinear operators and obtained elliptic modular form with interesting Fourier coefficients. In [12], D. Zagier studied the algebraic properties of these bilinear operators and called them as Rankin-Cohen brackets. In [13], following Rankin’s method, Zagier computed the n-th Rankin-Cohen bracket of a modular form g of weight k1 with the Eisenstein series of weight k2 and then computed the inner product of this Rankin-Cohen bracket with a cusp form f of weight k = k1 + k2 + 2n and showed that this inner product gives, upto a constant, the special value of the Rankin-Selberg convolution of f and g.