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3,154
On the Khintchine constant
 MATHEMATICS OF COMPUTATION
, 1997
"... We present rapidly converging series for the Khintchine constant and for general “Khintchine means” of continued fractions. We show that each of these constants can be cast in terms of an efficient freeparameter series, each series involving values of the Riemann zeta function, rationals, and logar ..."
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Cited by 9 (4 self)
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We present rapidly converging series for the Khintchine constant and for general “Khintchine means” of continued fractions. We show that each of these constants can be cast in terms of an efficient freeparameter series, each series involving values of the Riemann zeta function, rationals
On the Khintchine constant for centred continued fraction expansions
 Appl. Math. ENotes
, 2007
"... In this note, we consider a classical constant that arises in number theory, namely the Khintchine constant. This constant is closely related to the growth of partial quotients that appear in continued fraction expansions of reals. It equals the limit of the geometric mean of the partial quotient wh ..."
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Cited by 2 (0 self)
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In this note, we consider a classical constant that arises in number theory, namely the Khintchine constant. This constant is closely related to the growth of partial quotients that appear in continued fraction expansions of reals. It equals the limit of the geometric mean of the partial quotient
On the Best Constants in the Khintchine Inequality
, 1997
"... We show a selfcontained new proof for the best Bp constant in the Khintchine Inequality for p > 3 using only elementary calculus. ..."
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We show a selfcontained new proof for the best Bp constant in the Khintchine Inequality for p > 3 using only elementary calculus.
On the best constants in noncommutative Khintchinetype inequalities
 J. Funct. Analysis
"... Abstract. We obtain new proofs with improved constants of the Khintchinetype inequality with matrix coefficients in two cases. The first case is the Pisier and LustPiquard noncommutative Khintchine inequality for p = 1, where we obtain the sharp lower bound of √ 1 in the complex Gaussian case and ..."
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Cited by 9 (2 self)
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Abstract. We obtain new proofs with improved constants of the Khintchinetype inequality with matrix coefficients in two cases. The first case is the Pisier and LustPiquard noncommutative Khintchine inequality for p = 1, where we obtain the sharp lower bound of √ 1 in the complex Gaussian case and
Best constants in KahaneKhintchine inequalities in Orlicz spaces
 Math. Inst. Aarhus, Preprint Ser
, 1992
"... Several inequalities of KahaneKhintchine’s type in certain Orlicz spaces are proved. For this the classical symmetrization technique is used and four basically different methods have been presented. The first two are based on the wellknown estimates for subnormal random variables, see [9], the thi ..."
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Cited by 5 (4 self)
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], the third one is a consequence of a certain GaussianJensen’s majorization technique, see [6], and the fourth one is obtained by HaagerupYoungStechkin’s best possible constants in the classical Khintchine inequalities, see [4]. Moreover, by using the central limit theorem it is shown that this fourth
The Inequalities of Khintchine and Expanding Sphere of Their Action
"... 1. The strong law of large numbers of Borel and its refinements 2. The inequalities of Khintchine 3. Martingale extensions of Khintchine’s inequalities I ..."
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1. The strong law of large numbers of Borel and its refinements 2. The inequalities of Khintchine 3. Martingale extensions of Khintchine’s inequalities I
ON THE FAST KHINTCHINE SPECTRUM IN CONTINUED FRACTIONS
, 1208
"... Abstract. For x∈[0, 1), let x=[a1(x), a2(x),·· · ] be its continued fraction expansion with partial quotients{an(x), n≥1}. Letψ:N→N be a function withψ(n)/n→ ∞ as n→∞. In this note, the fast Khintchine spectrum, i.e., the Hausdorff dimension of the set E(ψ): = { 1 x∈[0, 1) : lim n→∞ψ(n) n∑ log a j( ..."
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Abstract. For x∈[0, 1), let x=[a1(x), a2(x),·· · ] be its continued fraction expansion with partial quotients{an(x), n≥1}. Letψ:N→N be a function withψ(n)/n→ ∞ as n→∞. In this note, the fast Khintchine spectrum, i.e., the Hausdorff dimension of the set E(ψ): = { 1 x∈[0, 1) : lim n→∞ψ(n) n∑ log a j
The KhintchineGroshev theorem for planar curves
, 1999
"... The analogue of the classical Khintchine{Groshev theorem, a fundamental result in metric Diophantine approximation, is established for smooth planar curves with nonvanishing curvature almost everywhere. ..."
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Cited by 3 (2 self)
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The analogue of the classical Khintchine{Groshev theorem, a fundamental result in metric Diophantine approximation, is established for smooth planar curves with nonvanishing curvature almost everywhere.
Matrix sparsification via the Khintchine inequality
"... Abstract. Given a matrix A ∈ R n×n, we present a simple, elementwise sparsification algorithm that zeroes out all sufficiently small elements of A, keeps all sufficiently large elements of A, and retains some of the remaining elements with probabilities proportional to the square of their magnitude ..."
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of their magnitudes. We analyze the approximation accuracy of the proposed algorithm using a powerful inequality bounding the norms of sums of random matrices, the socalled Khintchine inequality. As a result, we obtain improved bounds for the matrix sparsification problem. 1
1 A KHINTCHINETYPE THEOREM FOR
, 2005
"... Abstract. We obtain the convergence case of a Khintchine type theorem for a large class of hyperplanes. Our approach to the problem is from a dynamical viewpoint, and we modify a method due to Kleinbock and Margulis to prove the result. 1. ..."
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Abstract. We obtain the convergence case of a Khintchine type theorem for a large class of hyperplanes. Our approach to the problem is from a dynamical viewpoint, and we modify a method due to Kleinbock and Margulis to prove the result. 1.
Results 1  10
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3,154