Martin Raum: The Kohnen limit process

Abstract:
  Siegel modular forms are functions on specific locally symmetric spaces associated with symplectic groups. While Fourier expansions of holomorphic Siegel modular forms are being fruitfully applied to, for instance, Gromov-Witten invariants of Calabi-Yau manifolds and Moonshine from string theory, Fourier coefficients of real-analytic Siegel modular forms seldom receive attention from such areas. One reason is that there is few analytic tools to exhibit them.

In this talk, I present the Kohnen limit process, a novel tool to examine real-analytic Siegel modular forms of specific type. Its theory relies on both analytic considerations and facts from automorphic representation theory. I will sketch actual and potential applications of the Kohnen limit process.

This is based on joint work with Olav Richter