p-Adic Egyptian Fractions
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منابع مشابه
P-adic Continued Fractions and a P-adic Behavior of Quasi-periodic Dynamical Systems
In this paper we introduce p-adic continued fractions and its application to quasi-periodic dynamical systems. Investigating the recurrent properties of its orbits, we use the lattice theory, which has direct applications to cryptography. At last we show some numerical calculations of p-adic continued fractions and Gauss reduction algorithm by using the open source software Sage.
متن کاملApproximation Lattices of p - adic Numbers
Approximation lattices occur in a natural way in the study of rational approximations to p-adic numbers. Periodicity of a sequence of approximation lattices is shown to occur for rational and quadratic p-adic numbers. and for those only, thus establishing a p-adic analogue of Lagrange’s theorem on periodic continued fractions. Using approximation lattices we derive upper and lower bounds for th...
متن کاملIrrationality of some p-adic L-values
We give a proof of the irrationality of the p-adic zeta-values ζp(k) for p = 2, 3 and k = 2, 3. Such results were recently obtained by F.Calegari as an application of overconvergent p-adic modular forms. In this paper we present an approach using classical continued fractions discovered by Stieltjes. In addition we show irrationality of some other p-adic L-series values, and values of the p-adi...
متن کاملP -adic Continued Fractions
Continued fractions in R have a single definition and algorithms for approximating them are well known. There also exists a well known result which states that √ m, m ∈ Q, always has a periodic continued fraction representation. In Qp, the field of p-adics, however, there are competing and non-equivalent definitions of continued fractions and no single algorithm exists which always produces a p...
متن کاملp-adic Shearlets
The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.
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تاریخ انتشار 2015