Rational approximation to algebraic varieties and a new exponent of simultaneous approximation
نویسندگان
چکیده
منابع مشابه
Simultaneous Approximation and Algebraic Independence
We establish several new measures of simultaneous algebraic approximations for families of complex numbers (θ1, . . . , θn) related to the classical exponential and elliptic functions. These measures are completely explicit in terms of the degree and height of the algebraic approximations. In some instances, they imply that the fieldQ(θ1, . . . , θn) has transcendance degree≥2 overQ. This appro...
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We apply Padé approximation techniques to deduce lower bounds for simultaneous rational approximation to one or more algebraic numbers. In particular, we strengthen work of Osgood, Fel’dman and Rickert, proving, for example, that max {∣∣∣√2− p1/q∣∣∣ , ∣∣∣√3− p2/q∣∣∣} > q−1.79155 for q > q0 (where the latter is an effective constant). Some of the Diophantine consequences of such bounds will be d...
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ژورنال
عنوان ژورنال: Monatshefte für Mathematik
سال: 2016
ISSN: 0026-9255,1436-5081
DOI: 10.1007/s00605-016-0914-0