Jos Gunns

The Selberg L-functions under repeated differentiation.

The behaviour of functions (and in particular their zeros) under repeated differentiation has been studied, however, the constraints imposed to obtain 'nice' answers excludes the Riemann Xi-function and other similar functions. The Riemann Xi-function case has been studied using Fourier transforms, but the multiple Gamma functions in the analogous Selberg case meant that the same trick could not be immediately applied. Instead, the Fourier convolution theorem can be applied to reduce the number of integrals down to 1, at which point the original result about the Riemann case can be used.