Results 51 to 60 of about 2,483 (259)
Markov random walks on homogeneous spaces and Diophantine approximation on fractals [PDF]
Transactions of the American Mathematical Society, 2019 In the first part, using the recent measure classification results of Eskin–Lindenstrauss, we give a criterion to ensure a.s. equidistribution of empirical measures of an i.i.d.
Roland Prohaska, Cagri Sert
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Metric Diophantine approximation with congruence conditions [PDF]
International Journal of Number Theory, 2019 We prove a version of the Khinchin–Groshev theorem for Diophantine approximation of matrices subject to a congruence condition. The proof relies on an extension of the Dani correspondence to the quotient by a congruence subgroup.
Erez Nesharim, Ren'e Ruhr, Ronggang Shi
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Fibonacci Numbers with a Prescribed Block of Digits
Mathematics, 2020 In this paper, we prove that F 22 = 17711 is the largest Fibonacci number whose decimal expansion is of the form a b … b c … c . The proof uses lower bounds for linear forms in three logarithms of algebraic numbers and some tools from ...
Pavel Trojovský
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IET Information Security, 2021 A simultaneous Diophantine approximation (SDA) algorithm takes instances of the partial approximate common divisor (PACD) problem as input and outputs a solution.
Wonhee Cho, Jiseung Kim, Changmin Lee
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Expanding measures: Random walks and rigidity on homogeneous spaces
Forum of Mathematics, Sigma, 2023 Let G be a real Lie group, $\Lambda
Roland Prohaska +2 more
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On homogeneous and inhomogeneous Diophantine approximation over the fields of formal power series [PDF]
Pacific Journal of Mathematics, 2019 We prove over fields of power series the analogues of several Diophantine approximation results obtained over the field of real numbers. In particular we establish the power series analogue of Kronecker's theorem for matrices, together with a ...
Y. Bugeaud, Zhenliang Zhang
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Restricted diophantine approximation [PDF]
Journal of the Australian Mathematical Society, 1977 AbstractThe problem considered is that of approximating irrationals α by rationals p/q where p and q avoid certain congruence classes mod 2k for certain integers k. Results are obtained which give close bounds on a number c such that |α - p/q| < c/q2 has infinitely many solutions where p and q can be expressed as the sum of three squares.
openaire +2 more sources
Inhomogeneous Diophantine Approximation on M0-Sets with Restricted Denominators [PDF]
International mathematics research notices, 2019 Let $F \subseteq [0,1]$ be a set that supports a probability measure $\mu $ with the property that $ |\widehat{\mu }(t)| \ll (\log |t|)^{-A}$ for some constant $ A> 0 $. Let $\mathcal{A}= (q_n)_{n\in{\mathbb{N}}} $ be a sequence of natural numbers. If $
A. Pollington +3 more
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Mathematics, 2021 The Lattice String Approximation algorithm (or LSA algorithm) of M. L. Lapidus and M. van Frankenhuijsen is a procedure that approximates the complex dimensions of a nonlattice self-similar fractal string by the complex dimensions of a lattice self ...
Michel L. Lapidus +2 more
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How smooth is quantum complexity?
Journal of High Energy Physics, 2021 The “quantum complexity” of a unitary operator measures the difficulty of its construction from a set of elementary quantum gates. While the notion of quantum complexity was first introduced as a quantum generalization of the classical computational ...
Vir B. Bulchandani, S. L. Sondhi
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