Jaroslav Hančl

collaborators

4 papers

math.NT2024

On a Theorem of Nathanson on Diophantine Approximation

Jaroslav Hančl, Tho Phuoc Nguyen

In 1974, M. B. Nathanson proved that every irrational number $α$ represented by a simple continued fraction with infinitely many elements greater than or equal to $k$ is approximab…

math.NT2024

On a Theorem of Legendre on Diophantine Approximation

Jaroslav Hančl, Tho Phuoc Nguyen

Legendre's theorem states that every irreducible fraction $\frac{p}{q}$ which satisfies the inequality $α - \frac{p}{q} < \frac{1}{2 q ^{2}}$ is convergent to $α$ . Later…

math.NT2024

Linear independence of continued fractions with algebraic terms

Jaroslav Hančl, Mathias L. Laursen, Jitu Berhanu Leta

We give conditions on sequences of positive algebraic numbers ${a_{n, j}}_{n = 1}^{\infty}$ , $j = 1, \dots, M$ and number field $K$ to ensure that the numbers defined by the cont…

math.NT2014

On irrationality exponents of generalized continued fractions

Jaroslav Hancl, Kalle Leppälä, Tapani Matala-aho +1

We study how the asymptotic irrationality exponent of a given generalized continued fraction \[ \K_{n=1}^\infty \frac{a_n}{b_n}\,,\quad a_n, b_n\in \mathbb{Z}^+, \] behaves as a fu…