Results 31 to 40 of about 157,707 (146)
On approximation of p-adic numbers by p-adic algebraic numbers
Journal of Number Theory, 2005 18 ...
Beresnevich, V. +2 more
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Report on some recent advances in Diophantine approximation [PDF]
, 2009 A basic question of Diophantine approximation, which is the first issue we discuss, is to investigate the rational approximations to a single real number. Next, we consider the algebraic or polynomial approximations to a single complex number, as well as
Waldschmidt, Michel
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On the number of good approximations of algebraic numbers by algebraic numbers of bounded degree [PDF]
Acta Arithmetica, 1999 Define the absolute height of an algebraic number \(\beta\) by \(H(\beta)=|a_0|\prod_{i=1}^t\max (1,|\beta^{(i)}|)^{1/t}\), where \(t\) is the degree of \(\beta\), \(a_0\) is the leading coefficient of its minimal polynomial, and where \(\beta^{(1)}\ldots \beta^{(t)}\) are its conjugates. \textit{E. Wirsing} [Number Theory Institute 1969, Proc.
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Diophantine approximation by conjugate algebraic integers
, 2003 Building on work of Davenport and Schmidt, we mainly prove two results. The first one is a version of Gel'fond's transcendence criterion which provides a sufficient condition for a complex or $p$-adic number $\xi$ to be algebraic in terms of the ...
Roy, Damien, Waldschmidt, Michel
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Effective approximation to complex algebraic numbers by algebraic numbers of bounded degree
Transactions of the American Mathematical SocietyWe establish the first effective improvements on the Liouville inequality for approximation to complex non-real algebraic numbers by complex algebraic numbers of degree at most 4 4 .
Bajpai, Prajeet, Bugeaud, Yann
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Badly approximable numbers over imaginary quadratic fields
, 2018 We recall the notion of nearest integer continued fractions over the Euclidean imaginary quadratic fields $K$ and characterize the "badly approximable" numbers, ($z$ such that there is a $C(z)>0$ with $|z-p/q|\geq C/|q|^2$ for all $p/q\in K$), by ...
Hines, Robert
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Diagonal quartic surfaces and transcendental elements of the Brauer group [PDF]
, 2017 We exhibit central simple algebras over the function field of a diagonal quartic surface over the complex numbers that represent the 2-torsion part of its Brauer group.
Ieronymou, Evis
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, 2018 Steady state is an essential concept in reaction networks. Its stability reflects fundamental characteristics of several biological phenomena such as cellular signal transduction and gene expression.
Hasegawa, Yoshihiko, Van Vu, Tan
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Approximating algebraic numbers by j-invariants of elliptic curves [PDF]
Acta Arithmetica, 2008 is very close to 1728. Viewed in another light, then, this result says that j(EA,B) cannot be “too close” to 1728 (relative to the sizes of A and B) if EA,B(Q) contains a torsion point of order at least 5. In [5], the author proved similar results bounding |B| by a power of |A|, again for EA,B with certain torsion/isogeny structure.
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Two classes of real numbers and formal power series: quasi algebraic objects [PDF]
, 2014 Maurizio Citterio and Rodolfo Talamo, "Two classes of real numbers and formal power series: quasi algebraic objects", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste.
Citterio, Maurizio, Talamo, Rodolfo
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