# Bounded multiplicity for eigenvalues of a circular vibrating clamped plate

## TL;DR

This paper establishes an upper bound of six on the multiplicity of eigenvalues for a clamped circular plate, using a novel recursion formula, linear algebra, and transcendence theory.

## Contribution

It introduces a new recursion formula and applies advanced mathematical tools to bound eigenvalue multiplicities in a classical PDE problem.

## Key findings

- Eigenvalue multiplicity of the clamped disk is at most six.
- New recursion formula for eigenvalue analysis.
- Application of Siegel-Shidlovskii transcendence theorem.

## Abstract

We prove that no eigenvalue of the clamped disk can have multiplicity greater than six. Our method of proof is based on a new recursion formula, linear algebra arguments and a transcendency theorem due to Siegel and Shidlovskii.