Zeros of Fuchsian differential equations and infinitesimal Hilbert 16th problem

Funding source

Swedish Research Council - Vetenskapsrådet (VR)

Project Details

Start date: 01/01/2017
End date: 31/12/2020
Funding: 2800000 SEK


The main goal of this proposal is to find new effective upper bounds for
the number of zeros of solutions to Fuchsian differential equations
(with distinct real parts of all characteristic numbers at their
singularities) in simply-connected domains of the complex plane. The
existing upper bounds are double exponential in the relevant parameters
which make them hardly useful. I hope to obtain single exponential
bounds and apply them after proper modification to the infinitesimal
Hilbert 16th problem, where one needs to find uniform bounds for the
number of solutions of Picard- Fuchs equations of a fixed order with
bounded degrees of their coefficients. (Picard-Fuchs equations are
Fuchsian equations satisfying several additional restrictions.)

Last updated on 2017-05-10 at 11:48