On some polynomials and continued fractions arising in the theory of integrable systems
thesisposted on 06.07.2018 by Marie-Pierre J.E. Grosset
In order to distinguish essays and pre-prints from academic theses, we have a separate category. These are often much longer text based documents than a paper.
This thesis consists of two parts. In the first part an elliptic generalisation of the Bernoulli polynomials is introduced and investigated. We first consider the Faulhaber polynomials which are simply related to the even Bernoulli polynomials and generalise them in relatwn with the classical Lamé equation using the integrals of the Korteweg-de-Vries equation. An elliptic version of the odd Bernoulli polynomials is defined in relation to the quantum Euler top. These polynomials are applied to compute the Lamé spectral polynomials and the densities of states of the Lamé operators. In the second part we consider a special class of periodic continued fractions that we call α-fractions. [Continues.]
- Mathematical Sciences