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pro vyhledávání: '"David, Ofir"'
We show that the statistics of the continued fraction expansion of a randomly chosen rational in the unit interval, with a fixed large denominator $q$, approaches the Gauss-Kuzmin statistics with polynomial rate in $q$. This improves on previous resu
Externí odkaz:
http://arxiv.org/abs/2401.15586
Autor:
Elimelech, Rotem, David, Ofir, Mengual, Carlos De la Cruz, Kalisch, Rotem, Berndt, Wolfgang, Shalyt, Michael, Silberstein, Mark, Hadad, Yaron, Kaminer, Ido
Publikováno v:
PNAS 121 (25) e2321440121 (2024)
In recent decades, a growing number of discoveries in fields of mathematics have been assisted by computer algorithms, primarily for exploring large parameter spaces that humans would take too long to investigate. As computers and algorithms become m
Externí odkaz:
http://arxiv.org/abs/2308.11829
Autor:
David, Ofir
In this paper, we introduce the polynomial continued fraction, a close relative of the well-known simple continued fraction expansions which are widely used in number theory and in general. While they may not possess all the intriguing properties of
Externí odkaz:
http://arxiv.org/abs/2308.02567
Autor:
David, Ofir
We present a new structure called the "conservative matrix field", initially developed to elucidate and provide insight into the methodologies employed by Ap\'ery's in his proof of the irrationality of the Riemann zeta function at 3. This framework i
Externí odkaz:
http://arxiv.org/abs/2303.09318
Formulas involving fundamental mathematical constants had a great impact on various fields of science and mathematics, for example aiding in proofs of irrationality of constants. However, the discovery of such formulas has historically remained scarc
Externí odkaz:
http://arxiv.org/abs/2212.09470
Autor:
David, Ofir
In this notes we show how a problem regarding continued fractions of rational numbers, lead to several phenomena in number theory and dynamics, and eventually to the problem of shearing of divergent diagonal orbits in the space of adelic lattices. Fi
Externí odkaz:
http://arxiv.org/abs/1909.00053
Autor:
David, Ofir
We use Margulis' construction together with lattice counting arguments to build Cayley graphs on $\mathrm{SL}_{2}\left(\mathbb{F}_{p}\right),\;p\to\infty$ which are d-regular graphs with girth $\geq\frac{2}{3}\frac{\ln\left(n\right)}{\ln\left(d-1\rig
Externí odkaz:
http://arxiv.org/abs/1907.06936
Autor:
David, Ofir
The local to global property for an equation $\psi$ over a group G asks to show that $\psi$ is solvable in G if and only if it is solvable in every finite quotient of G. In this paper we focus that in order to prove this local to global property for
Externí odkaz:
http://arxiv.org/abs/1907.05968
Akademický článek
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Autor:
David, Ofir, Shapira, Uri
We consider divergent orbits of the group of diagonal matrices in the space of lattices in Euclidean space. We define two natural numerical invariants of such orbits: The discriminant - an integer - and the type - an integer vector. We then study the
Externí odkaz:
http://arxiv.org/abs/1710.05242