Thesis-2007-Grosset.pdf (2.24 MB)
On some polynomials and continued fractions arising in the theory of integrable systems
thesis
posted on 2018-07-06, 11:35 authored by Marie-Pierre J.E. GrossetThis 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.]
History
School
- Science
Department
- Mathematical Sciences
Publisher
© Marie-Pierre J.E. GrossetPublisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Publication date
2007Notes
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.Language
- en