We present an elliptic version of Selberg's integral formula.

In our previous works “Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants” (by M.Ishikawa, H. Tagawa and J. Zeng, J. Combin. Theory Ser. A, 120, 2013, 1263–1284) we have proposed several ways to evaluate certain Catalan-Hankel Pffafians and also formulated several conjectures. In this work we propose a new approach to compute these Catalan-Hankel Pffafians using Sel...

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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.