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Cryptanalysis of short RSA secret exponents
 IEEE Trans. Inform. Theory
, 1990
"... Abstract. A cryptanalytic attack on the use of short RSA secret exponents is described. This attack makes use of an algorithm based on continued fractions which finds the numerator and denominator of a fraction in polynomial time when a close enough estimate of the fraction is known. The public expo ..."
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Cited by 167 (1 self)
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Abstract. A cryptanalytic attack on the use of short RSA secret exponents is described. This attack makes use of an algorithm based on continued fractions which finds the numerator and denominator of a fraction in polynomial time when a close enough estimate of the fraction is known. The public
Semicontinuity of complex singularity exponents and KählerEinstein metrics on Fano orbifolds
, 2000
"... ..."
Open problems in variable exponent Lebesgue and Sobolev spaces
 IN: ”FUNCTION SPACES, DIFFERENTIAL OPERATORS AND NONLINEAR ANALYSIS”, PROC. CONFERENCE HELD IN MILOVY, BOHEMIANMORAVIAN UPLANDS, MAY 28JUNE 2, 2004, MATH. INST. ACAD. SCI. CZECH
, 2005
"... In this article we provide an overview of several open problems in variable exponent spaces. The problems are related to boundedness of the maximal operator, interpolation theory, density of smooth functions and Sobolev embeddings. We also extend a result on complex interpolation to the variable e ..."
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Cited by 68 (4 self)
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exponent setting and give an example of a continuous exponent p for which W 1,p(·) does not embed into Lp.
On Khintchine exponents and Lyapunov exponents of continued fractions
, 2008
"... Assume that x ∈ [0,1) admits its continued fraction expansion x = [a1(x), a2(x), · · ·]. The Khintchine exponent γ(x) of x is defined by 1 Pn γ(x): = lim n→ ∞ n j=1 log aj(x) when the limit exists. Khintchine spectrum dim Eξ is fully studied, where Eξ: = {x ∈ [0, 1) : γ(x) = ξ} (ξ ≥ 0) and dim d ..."
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Cited by 15 (8 self)
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Assume that x ∈ [0,1) admits its continued fraction expansion x = [a1(x), a2(x), · · ·]. The Khintchine exponent γ(x) of x is defined by 1 Pn γ(x): = lim n→ ∞ n j=1 log aj(x) when the limit exists. Khintchine spectrum dim Eξ is fully studied, where Eξ: = {x ∈ [0, 1) : γ(x) = ξ} (ξ ≥ 0) and dim
Continuity of the Lyapunov exponent for
, 2001
"... quasiperiodic operators with analytic potential. ..."
Continuity of the Lyapunov exponent for quasiperiodic operators with analytic potential.
, 2001
"... this paper we study continuity of the Lyapunov exponent associated with 1D quasiperiodic operators. Assume v real analytic on T. Let v : T ! R : Consider an SL 2 (R) valued function A(x; E) = v(x) E 1 1 0 ; x 2 T: (1.1) Set MN (E; x; !) = A(S j x); Sx = x + !; LN (E; !) = log kMN ..."
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Cited by 45 (8 self)
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this paper we study continuity of the Lyapunov exponent associated with 1D quasiperiodic operators. Assume v real analytic on T. Let v : T ! R : Consider an SL 2 (R) valued function A(x; E) = v(x) E 1 1 0 ; x 2 T: (1.1) Set MN (E; x; !) = A(S j x); Sx = x + !; LN (E; !) = log k
CONTINUITY OF THE LYAPUNOV EXPONENTS FOR QUASIPERIODIC COCYCLES
"... Abstract. Consider the Banach manifold of real analytic linear cocycles with values in the general linear group of any dimension and base dynamics given by a Diophantine translation on the circle. We prove a precise higher dimensional Avalanche Principle and use it in an inductive scheme to show th ..."
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Cited by 6 (1 self)
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that the Lyapunov spectrum blocks associated to a gap pattern in the Lyapunov spectrum of such a cocycle are locally Hölder continuous. Moreover, we show that all Lyapunov exponents are continuous everywhere in this Banach manifold, irrespective of any gap pattern in their spectrum. These results also hold
On irrationality exponents of generalized continued fractions
"... Abstract We study how the asymptotic irrationality exponent of a given generalized continued fraction behaves as a function of growth properties of partial coefficient sequences ( ) and ( ). ..."
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Abstract We study how the asymptotic irrationality exponent of a given generalized continued fraction behaves as a function of growth properties of partial coefficient sequences ( ) and ( ).
and critical exponents
, 1998
"... With the help of variational perturbation theory we continue the renormalization constants of f 4theories in 4ye dimensions to infinitely strong bare couplings g and find their power behavior in g, thereby determining all critical0 0 exponents without the standard renormalization group techniques. ..."
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With the help of variational perturbation theory we continue the renormalization constants of f 4theories in 4ye dimensions to infinitely strong bare couplings g and find their power behavior in g, thereby determining all critical0 0 exponents without the standard renormalization group techniques
Exponents of Diophantine Approximation and Sturmian Continued Fractions
, 2004
"... Let ξ be a real number and let n be a positive integer. We define four exponents of Diophantine approximation, which complement the exponents wn(ξ) and w ∗ n (ξ) defined by Mahler and Koksma. We calculate their six values when n = 2 and ξ is a real number whose continued fraction expansion coincid ..."
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Cited by 26 (10 self)
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Let ξ be a real number and let n be a positive integer. We define four exponents of Diophantine approximation, which complement the exponents wn(ξ) and w ∗ n (ξ) defined by Mahler and Koksma. We calculate their six values when n = 2 and ξ is a real number whose continued fraction expansion
Results 1  10
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1,267