Results 11 to 20 of about 157,970 (240)
Approximation of complex algebraic numbers by algebraic numbers of bounded degree
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2007 We investigate how well complex algebraic numbers can be approximated by algebraic numbers of degree at most n. We also investigate how well complex algebraic numbers can be approximated by algebraic integers of degree at most n+1.
Bugeaud, Yann, Evertse, Jan-Hendrik
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Approximation of an algebraic number by products of rational numbers and units [PDF]
Journal of the Australian Mathematical Society, 2013 We relate a previous result of ours on families of Diophantine equations having only trivial solutions with a result on the approximation of an algebraic number by products of rational numbers and units.
Levesque, Claude, Waldschmidt, Michel
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Simultaneous approximation of a real number by all conjugates of an algebraic number [PDF]
Acta Arithmetica, 2007 Using a method of H. Davenport and W. M. Schmidt, we show that, for each positive integer n, the ratio 2/n is the optimal exponent of simultaneous approximation to real irrational numbers 1) by all conjugates of algebraic numbers of degree n, and 2) by ...
Alain, Guillaume
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Approximation to real numbers by cubic algebraic integers. II [PDF]
Annals of Mathematics, 2003 In 1969, H. Davenport and W. M. Schmidt studied the problem of approximation to a real number by algebraic integers of degree at most three. They did so, using geometry of numbers, by resorting to the dual problem of finding simultaneous approximations to and ^2 by rational numbers with the same denominator.
Damien Roy
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On approximation of real numbers by real algebraic numbers [PDF]
Acta Arithmetica, 1999 Let \(\mathbb A_n\) be the set of real algebraic numbers of degree \(n\) and \(H(\alpha)\) be the height of \(\alpha\in \mathbb A_n\). A `best possible' regular system \((\mathbb A_n,N)\), where \(N(\alpha)= (H(\alpha)/ (1+|\alpha|)^n)^{n+1}\), is obtained for approximating real numbers by numbers \(\alpha\) in \(A_n\).
Victor V Beresnevich
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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.
Wolfgang M Schmidt
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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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Approximation to real numbers by algebraic integers [PDF]
Acta Arithmetica, 1969 Davenport, Harold, Schmidt, Wolfgang M.
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Scientific Reports, 2021 Block cipher has been a standout amongst the most reliable option by which data security is accomplished. Block cipher strength against various attacks relies on substitution boxes.
Muhammad Fahad Khan +3 more
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On Joint Universality in the Selberg–Steuding Class
Mathematics, 2023 The famous Selberg class is defined axiomatically and consists of Dirichlet series satisfying four axioms (Ramanujan hypothesis, analytic continuation, functional equation, multiplicativity).
Roma Kačinskaitė +2 more
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