The values of L-functions at special points have been the subject of intensive studies. For example, a good positive lower bound for the central value of Hecke L-functions would rule out the existence of the Landau-Siegel zero, see the notable paper [IS]; the nonvanishing of certain Rankin-Selberg L-functions is a crucial ingredient in the current development of the generalized Ramanujan conjec...

Let π = ⊗πv and π ′ = ⊗π ′ v be two irreducible, automorphic, cuspidal representations of GLm (AK). Using the logarithmic zero-free region of Rankin-Selberg L-function, Moreno established the analytic strong multi-plicity one theorem if at least one of them is self-contragredient, i.e. π and π ′ will be equal if they have finitely many same local components πv, π ′ v , for which the norm of pla...

Abstract. Following Rankin’s method, D. 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. This...

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 ...

In this paper, we prove some period relations for the ratio of Deligne’s periods for certain tensor product motives. These period relations give a motivic interpretation for certain algebraicity results for ratios of successive critical values for Rankin–Selberg L-functions for GLn × GLn′ proved by Günter Harder and the second author.

A standard zero free region is obtained for Rankin Selberg L-functions L(s, f×f) where f is a tempered Maass form on GL(n) and f is not necessarily self dual. The method is based on the theory of Eisenstein series generalizing a work of Sarnak. §