In a recent important paper, Hoffstein and Hulse [14] generalized the notion of Rankin-Selberg convolution L-functions by defining shifted convolution L-functions. We investigate symmetrized versions of their functions, and we prove that the generating functions of certain special values are linear combinations of weakly holomorphic quasimodular forms and “mixed mock modular” forms.

We specify sufficient conditions for the square modulus of the local parameters of a family of GLn cusp forms to be bounded on average. These conditions are global in nature and are satisfied for n ≤ 4. As an application, we show that Rankin-Selberg L-functions on GLn1 × GLn2 , for ni ≤ 4, satisfy the standard convexity bound.

We consider the family of Rankin-Selberg convolution L-functions of a fixed SL(3,Z) Maass form with the family of Hecke-Maass cusp forms on SL(2,Z). We estimate the second moment of this family of L-functions with a “long” integration in t-aspect. These L-functions are distinguished by their high degree (12) and large conductors (of size T ).

In this paper we calculate the asymptotics of various moments of the central values of Rankin-Selberg convolution L-functions of large level, thus generalizing the results and methods of W. Duke, J. Friedlander, and H. Iwaniec and of the authors. Consequences include convexity-breaking bounds, nonvanishing of a positive proportion of central values, and linear independence results for certain H...

We specify sufficient conditions for the square modulus of the local parameters of a family of GLn cusp forms to be bounded on average. These conditions are global in nature and are satisfied for n ≤ 4. As an application, we show that Rankin-Selberg L-functions on GLn1 × GLn2 , for ni ≤ 4, satisfy the standard convexity bound.

We evaluate a rigid analytical analogue of the Beilinson-Bloch-Deligne regulator on certain explicit elements in the K2 of Drinfeld modular curves, constructed from analogues of modular units, and relate its value to special values of L-series using the Rankin-Selberg method.

Abstract In [14], Jacquet–Piatetskii-Shapiro–Shalika defined a family of compact open subgroups p -adic general linear groups indexed by nonnegative integers and established the theory local newforms for irreducible generic representations. this paper, we extend their results to all To do this, define new certain tuples integers. For proof, introduce Rankin–Selberg integrals Speh

We use Poincare series for massive Maass-Jacobi forms to define a "massive theta lift", and apply it the examples of constant function modular invariant j-function, with Siegel-Narain as integration kernel. These integrals are deformations known one-loop string threshold corrections. Our lifts fall off exponentially, so some Rankin-Selberg finite without Zagier renormalization.