有限Diophantine逼近与Fibonacci多项式(英文)

Finite Diophantine Approximation and Fibonacci Polynomials

设x为一无理数具简单的连分式展开x = [a0, a1, a2,…, an].若对无穷多个是标k有ak> n则至少有m个解p/q(p与q互素)使不等式 x - p/q <Cm(1n)q2成立,此处Cm(h) = n2+ 41 +n4+ 4n2+ 2 + (n2+1 2)n n2+ 42m- 1.

Let x be an irrational number with simple continued fraction expansion x=[a0;a1,a1,…,ak,…].If ak≥n for infinitely many indices k, then there are at least m solutions p/q in coprime integers p,q to the inequality ｜x-p/q｜〈1/Cm（n）q^2,where Cm（n）equals to √n^2＋4（1＋1/（n^4＋4n^2＋2＋（n^2＋2）n√n^2＋4/2）^m-1）