Add to ORKGThis 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.
AbstractSeveral classical combinatorial quantities—including factorials, Bell numbers, tangent numbe...
We define an infinite sequence of generalizations, parametrized by an integer m ≥ 1, of the Stieltj...
Title: Computational problems of elementary number theory Author: Mgr. Jiří Widž Department: Departm...
This thesis consists of two parts. In the first part an elliptic generalisation of the Bernoulli pol...
For a complex polynomial D(t) of even degree, one may define the continued fraction of D(t). This wa...
A generalisation of the Faulhaber polynomials and Bernoulli numbers related to elliptic curves is in...
A generalisation of the odd Bernoulli polynomials related to the quantum Euler top is introduced and...
AbstractWe show that the universal continued fraction of the Stieltjes-Jacobi type is equivalent to ...
These are notes from the minicourse given by Umberto Zannier (Scuola Normale Superiore di Pisa). The...
In this paper we show how to apply various techniques and theorems (including Pincherle’s theorem, a...
In the first part of this thesis, we show that a wide range of the properties of the roots of transl...
Continued fractions are systematically studied in number theory, dynamical systems, and ergodic theo...
The classical theory of real continued fractions has a nearly perfect analogue in the function field...
Continued fractions whose elements are polynomial sequences have been carefully studied mostly in th...
It is widely believed that the continued fraction expansion of every irrational algebraic number $\a...
AbstractSeveral classical combinatorial quantities—including factorials, Bell numbers, tangent numbe...
We define an infinite sequence of generalizations, parametrized by an integer m ≥ 1, of the Stieltj...
Title: Computational problems of elementary number theory Author: Mgr. Jiří Widž Department: Departm...
This thesis consists of two parts. In the first part an elliptic generalisation of the Bernoulli pol...
For a complex polynomial D(t) of even degree, one may define the continued fraction of D(t). This wa...
A generalisation of the Faulhaber polynomials and Bernoulli numbers related to elliptic curves is in...
A generalisation of the odd Bernoulli polynomials related to the quantum Euler top is introduced and...
AbstractWe show that the universal continued fraction of the Stieltjes-Jacobi type is equivalent to ...
These are notes from the minicourse given by Umberto Zannier (Scuola Normale Superiore di Pisa). The...
In this paper we show how to apply various techniques and theorems (including Pincherle’s theorem, a...
In the first part of this thesis, we show that a wide range of the properties of the roots of transl...
Continued fractions are systematically studied in number theory, dynamical systems, and ergodic theo...
The classical theory of real continued fractions has a nearly perfect analogue in the function field...
Continued fractions whose elements are polynomial sequences have been carefully studied mostly in th...
It is widely believed that the continued fraction expansion of every irrational algebraic number $\a...
AbstractSeveral classical combinatorial quantities—including factorials, Bell numbers, tangent numbe...
We define an infinite sequence of generalizations, parametrized by an integer m ≥ 1, of the Stieltj...
Title: Computational problems of elementary number theory Author: Mgr. Jiří Widž Department: Departm...