Approximation of p-adic numbers by algebraic numbers of bounded degree
Journal of Number Theory, 1978 AbstractThe approximation of p-adic numbers by algebraic numbers of bounded degree is studied. Results similar to those obtained by Wirsing and by Davenport and Schmidt in the real case are proved in the p-adic case. Unlike the real case the expected best exponent is not obtained when approximating by quadratic irrationals.
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On approximation of real numbers by algebraic numbers of bounded degree
Journal of Number Theory, 2007 Dirichlet proved that, for any real irrational number \(\xi\), there exist infinitely many rational numbers \(\frac{p}{q}\) such that \(|\xi-\frac{p}{q}|2\). Let \(\mathbf A_n, \;n>2\) denote the set of algebraic numbers of degree \(\leq n\). Let \(\alpha\in \mathbf A_n\) and \(H(\alpha)\) the height of \(\alpha\), that is the largest absolute value of
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Simultaneous approximation to algebraic numbers by elements of a number field
Monatshefte f�r Mathematik, 1975 A special case of the main result is as follows. Given a number fieldK a number ɛ>0 and real or complex algebraic numbers ξ1,...,ξn with 1, ξ1,...,ξn linearly independent overK, there are only finitely many α=(α1,...,αn) with components inK and with |ξ1,...,α1| whereH(α) is a suitably defined height.
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On the approximation of the values of exponential function and logarithm by algebraic numbers
, 2000 17 pages. See also http://www.math.jussieu.fr/~miw/articles/ps/Nesterenko.ps and http://www.math.jussieu.fr/~nesteren/
Nesterenko, Yu., Waldschmidt, M.
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Approximation to real numbers by algebraic integers [PDF]
Acta Arithmetica, 1969 Davenport, Harold, Schmidt, Wolfgang M.
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Approximations to real algebraic numbers by algebraic numbers of smaller degree [PDF]
Pacific Journal of Mathematics, 1981 openaire +2 more sources
Approximation of algebraic numbers by algebraic numbers.
Michigan Mathematical Journal, 1961 openaire +2 more sources
On approximation to a real number by algebraic numbers of bounded degree
Annals of MathematicsIn his seminal 1961 paper, Wirsing studied how well a given transcendental real number $ξ$ can be approximated by algebraic numbers $α$ of degree at most $n$ for a given positive integer $n$, in terms of the so-called naive height $H(α)$ of $α$. He showed that the infimum $ω^*_n(ξ)$ of all $ω$ for which infinitely many such $α$ have $|ξ-α| \le H(α)^{-ω-
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Surprisal Analysis-Based Compaction of Entangled Molecular States of Maximal Entropy. [PDF]
Entropy (Basel)Hamilton JR, Remacle F, Levine RD.
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Computer-assisted construction of Ramanujan-Sato series for 1 over π. [PDF]
Ramanujan JHemmecke R, Paule P, Radu CS.
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