From among $n$ conjugate algebraic integers, $n - 1$ can be approximately given
نویسندگان
چکیده
منابع مشابه
Approximately $n$-order linear differential equations
We prove the generalized Hyers--Ulam stability of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.
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Building on the 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 ξ to be algebraic in terms of the existence of polynomials of bounded degree taking small values at ξ together with most of their derivatives. The second one, which follows from this crit...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1947
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1947-08772-3