Ramanujan's master theorem for radial sections of line bundle over noncompact symmetric spaces

TL;DR

This paper extends Ramanujan's Master theorem to radial sections of line bundles over noncompact symmetric spaces, specifically the Poincaré upper half plane and complex hyperbolic spaces.

Contribution

It establishes analogues of Ramanujan's Master theorem for these specific geometric settings, advancing the understanding of harmonic analysis on noncompact symmetric spaces.

Findings

Derived new integral formulas for radial sections

Extended Ramanujan's theorem to complex hyperbolic spaces

Provided analytical tools for harmonic analysis on line bundles

Abstract

We prove analogues of Ramanujan's Master theorem for the radial sections of the line bundles over the Poincar\'{e} upper half plane $\mathrm{SL}(2, \R)/\mathrm{SO}(2)$ and over the complex hyperbolic spaces $\mathrm {SU}(1, n)/ S(\mathrm{U}(1) \times \mathrm{U}(n))$.