Prof. Walter Bergweiler，University of Kiel, Germany

We consider the frequency of zeros of solutions of the differential equation w′′+Aw=0 with an entire coefficient A. First we review the results for a polynomial coefficient A. Next we discuss various results due to Bank, Laine and others dealing with the case that A is a transcendental entire function. We then describe a new method to construct coefficients A for which there are two linearly independent solutions with relatively few zeros. We start with certain coefficients A for which the solutions can be given explicitly and then sketch how solutions for different coefficients can be “glued” using quasiconformal maps. The method yields the solution of a problem posed by Bank and Laine. This is joint work with Alexandre Eremenko.