Results 11 to 20 of about 343 (48)
Pattern Classification of Continued Fractions With Square Number as Base
Journal of Physics: Conference Series, 2019 In number theory, study of number sequences is an enthusiastic area. Among these the sequence of polygonal numbers gives a unique richness in is applicability. Polygonal numbers which have both order, rank of are of various dimensions. Here, the study is
A. Venkatachalam, P. Balamurugan
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Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018 The Foias constant, a true mathematical gem, is generalized to a host of similar numbers. As is the case with all significant mathematics it is the underlying method, due to Foias, that matters.
Anghel Nicolae
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Hyperelliptic curves, continued fractions, and Somos sequences [PDF]
, 2006 We detail the continued fraction expansion of the square root of a monic polynomials of even degree. We note that each step of the expansion corresponds to addition of the divisor at infinity, and interpret the data yielded by the general expansion.
van der Poorten, Alfred J.
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Asymptotic formula for the moments of Minkowski question mark function in the interval [0,1]
, 2008 In this paper we prove the asymptotic formula for the moments of Minkowski question mark function, which describes the distribution of rationals in the Farey tree. The main idea is to demonstrate that certain a variation of a Laplace method is applicable
A. Denjoy +5 more
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Equality cases of the Alexandrov–Fenchel inequality are not in the polynomial hierarchy
Forum of Mathematics, PiDescribing the equality conditions of the Alexandrov–Fenchel inequality [Ale37] has been a major open problem for decades. We prove that in the case of convex polytopes, this description is not in the polynomial hierarchy unless the polynomial hierarchy ...
Swee Hong Chan, Igor Pak
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Ramanujan and Extensions and Contractions of Continued Fractions
, 2004 If a continued fraction $K_{n=1}^{\infty} a_{n}/b_{n}$ is known to converge but its limit is not easy to determine, it may be easier to use an extension of $K_{n=1}^{\infty}a_{n}/b_{n}$ to find the limit. By an extension of $K_{n=1}^{\infty} a_{n}/b_{n}$
B.C. Berndt +13 more
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A security analysis of two classes of RSA-like cryptosystems
Journal of Mathematical CryptologyLet N=pqN=pq be the product of two balanced prime numbers pp and qq. In Elkamchouchi et al. (Extended RSA cryptosystem and digital signature schemes in the domain of Gaussian integers. In: ICCS 2002. vol. 1. IEEE Computer Society; 2002. p.
Cotan Paul, Teşeleanu George
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, 2009 This paper continues investigations on the integral transforms of the Minkowski question mark function. In this work we finally establish the long-sought formula for the moments, which does not explicitly involve regular continued fractions, though it ...
F. Ryde +11 more
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, 2018 For each positive integer $n$ it is shown how to construct a finite collection of multivariable polynomials $\{F_{i}:=F_{i}(t,X_{1},..., X_{\lfloor \frac{n+1}{2} \rfloor})\}$ such that each positive integer whose squareroot has a continued fraction ...
Bernstein +7 more
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Polynomial estimates, exponential curves and Diophantine approximation
, 2010 Let $\alpha\in(0,1)\setminus{\Bbb Q}$ and $K=\{(e^z,e^{\alpha z}):\,|z|\leq1\}\subset{\Bbb C}^2$. If $P$ is a polynomial of degree $n$ in ${\Bbb C}^2$, normalized by $\|P\|_K=1$, we obtain sharp estimates for $\|P\|_{\Delta^2}$ in terms of $n$, where ...
Coman, Dan, Poletsky, Evgeny A.
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