Event № 819
A celebrated result of C.L. Siegel from 1929 shows that the multiplicity of eigenvalues for the Laplace eigenfunctions on the unit disk is at most two. To show this, Siegel shows that positive zeros of Bessel functions are transcendental. We study the fourth order clamped plate problem, showing that the multiplicity of eigenvalues is at most by six. In particular, the multiplicity is uniformly bounded. Our method is based on Siegel-Shidlovskii theory and new recursion formulas.This is joint work with Yuri Lvovski.