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pro vyhledávání: '"Kontorovich, Alex V."'
Publikováno v:
in: The Ultimate Challenge: The 3x+1 problem, Amer. Math. Soc.: Providence 2010, pp. 131--188
This paper discusses stochastic models for predicting the long-time behavior of the trajectories of orbits of the 3x+1 problem and, for comparison, the 5x+1 problem. The stochastic models are rigorously analyzable, and yield heuristic predictions (co
Externí odkaz:
http://arxiv.org/abs/0910.1944
Autor:
Kontorovich, Alex V.
Publikováno v:
Duke Math. J. 149, no. 1 (2009), 1-36
We develop novel techniques using abstract operator theory to obtain asymptotic formulae for lattice counting problems on infinite-volume hyperbolic manifolds, with error terms which are uniform as the lattice moves through "congruence" subgroups. We
Externí odkaz:
http://arxiv.org/abs/0712.1391
Autor:
Kontorovich, Alex V., Sinai, Yakov G.
Publikováno v:
Bulletin of the Brazilian Mathematical Society, Volume 33, Issue 2, Jul 2002, Pages 213 - 224
The (3x+1)-Map, T, acts on the set, Pi, of positive integers not divisible by 2 or 3. It is defined by T(x) = (3x+1)/2^k, where k is the largest integer for which T(x) is an integer. The (3x+1)-Conjecture asks if for every x in Pi there exists an int
Externí odkaz:
http://arxiv.org/abs/math/0601622
Autor:
Kontorovich, Alex V.
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Externí odkaz:
http://arxiv.org/abs/math/0507571
Autor:
Kontorovich, Alex V.
Selberg identified the "parity" barrior, that sieves alone cannot distinguish between integers having an even or odd number of factors. We give here a short and self-contained demonstration of parity breaking using bilinear forms, modeled on the Twin
Externí odkaz:
http://arxiv.org/abs/math/0507569
Publikováno v:
Journal of Number Theory 117 (2006), 1--13
For every positive integer $n$, the quantum integer $[n]_q$ is the polynomial $[n]_q = 1 + q + q^2 + ... + q^{n-1}.$ A quadratic addition rule for quantum integers consists of sequences of polynomials $\mathcal{R}' = \{r'_n(q)\}_{n=1}^{\infty}$, $\ma
Externí odkaz:
http://arxiv.org/abs/math/0503177
Publikováno v:
Acta Arithmetica 120 (2005), no. 3, 269-297
We show the leading digits of a variety of systems satisfying certain conditions follow Benford's Law. For each system proving this involves two main ingredients. One is a structure theorem of the limiting distribution, specific to the system. The ot
Externí odkaz:
http://arxiv.org/abs/math/0412003
Autor:
Kontorovich, Alex V.
Publikováno v:
Multiple Dirichlet Series, L-functions & Automorphic Forms; 2012, p287-298, 12p
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