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pro vyhledávání: '"11A55"'
Autor:
Bernardini, Riccardo
In this paper we are interested in the class numbers of a family of real quadratic fields for which the square roots of the discriminants have a known expansion in continued fraction. In particular we prove that $h(D)>1$, with possibly a finite numbe
Externí odkaz:
http://arxiv.org/abs/2412.06351
Autor:
Stange, Katherine E.
These notes cover and expand upon the material for two summer schools: The first, which was held at CIRM, Marseille, France, July 10-14, 2023, as part of "Renormalization and Visualization for packing, billiard and surfaces", was titled "Number theor
Externí odkaz:
http://arxiv.org/abs/2412.02050
Autor:
Yasutomi, Shin-ichi
J. Hurwitz introduced an algorithm that generates a continued fraction expansion for complex numbers $\alpha \in \mathbb{C}$, where the partial quotients belong to $(1+i)\mathbb{Z}[i]$. J. Hurwitz's work also provides a result analogous to Lagrange's
Externí odkaz:
http://arxiv.org/abs/2410.16683
We prove some new modular identities for the Rogers\textendash Ramanujan continued fraction. For example, if $R(q)$ denotes the Rogers\textendash Ramanujan continued fraction, then \begin{align*}&R(q)R(q^4)=\dfrac{R(q^5)+R(q^{20})-R(q^5)R(q^{20})}{1+
Externí odkaz:
http://arxiv.org/abs/2410.17110
A few years ago Morier-Genoud and Ovsienko introduced an interesting quantization of the real numbers as certain power series in a quantization parameter $q.$ It is known now that the golden ratio has minimal radius among all these series. We study t
Externí odkaz:
http://arxiv.org/abs/2410.15666
Publikováno v:
Czechoslovak Mathematical Journal 73.2 (2023): 603-611
It is clear that every rational surgery on a Hopf link in $3$-sphere is a lens space surgery. In this note we give an explicit computation which lens space is a resulting manifold. The main tool we use is the calculus of continued fractions. As a cor
Externí odkaz:
http://arxiv.org/abs/2410.13014
Autor:
Garrity, Thomas, Osterman, Otto Vaughn
We study the complexity of S-adic sequences corresponding to a family of 216 multi-dimensional continued fractions maps, called Triangle Partition maps (TRIP maps), with an emphasis on those with low upper bounds on complexity. Our main result is to
Externí odkaz:
http://arxiv.org/abs/2410.02032
Autor:
Zindulka, Mikuláš
In this paper, we study partitions of totally positive integral elements $\alpha$ in a real quadratic field $K$. We prove that for a fixed integer $m \geq 1$, an element with $m$ partition exists in almost all $K$. We also obtain an upper bound for t
Externí odkaz:
http://arxiv.org/abs/2409.18080
Autor:
Kalinin, Nikita
New formulae for a summation over a positive part of $SL(2,\mathbb Z)$ are presented. Such formulae can be written for any convex curve. We present several formulae where $\pi$ is obtained.
Externí odkaz:
http://arxiv.org/abs/2409.10592
Autor:
Karpenkov, Oleg, Pratoussevitch, Anna
The construction of the Farey tessellation in the hyperbolic plane starts with a finitely generated group of symmetries of an ideal triangle, i.e. a triangle with all vertices on the boundary. It induces a remarkable fractal structure on the boundary
Externí odkaz:
http://arxiv.org/abs/2409.01621