Introduction to Diophantine Approximation
نویسندگان
چکیده
منابع مشابه
Introduction to Diophantine Approximation
In this article we formalize some results of Diophantine approximation, i.e. the approximation of an irrational number by rationals. A typical example is finding an integer solution (x, y) of the inequality |xθ − y| ¬ 1/x, where θ is a real number. First, we formalize some lemmas about continued fractions. Then we prove that the inequality has infinitely many solutions by continued fractions. F...
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Let us come back to the problem which was considered in § 1.4.1 and solved by Hermite (Proposition 1.20): Given two integers n0 ≥ 0, n1 ≥ 0, find two polynomials A and B with A of degree ≤ n0 and B of degree ≤ n1 such that the function R(z) = B(z)e −A(z) has a zero at the origin of multiplicity ≥ N + 1 with N = n0 + n1. From § 1.4.3 one easily deduces that there is a non-trivial solution, and i...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2015
ISSN: 1898-9934
DOI: 10.1515/forma-2015-0010