| 于秀源,沈忠华.连分数对数的线形型下界[J].数学年刊A辑,2009,30(3):353~358 |
| 连分数对数的线形型下界 |
| The Lower Bound of the Linear Form of Logarithms of Continued Fractions |
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| DOI： |
| 中文关键词: 连分数 对数 线形型 下界 |
| 英文关键词:Continued fraction, Logarithm, Linear form, Lower bound |
| 基金项目:国家自然科学基金，浙江省自然科学基金(No.103060)资助的项目 |
| Author Name | Affiliation | E-mail | | YU Xiuyuan | Department of Mathematics, Hangzhou Normal University, Hangzhou 310036,
China
Deprtment of Mathematics, Zhe Xi Branch of Zhejiang Industry Uni-
versity, Quzhou 324000, Zhejiang, China. | ahtshen@126.com | | SHEN Zhonghua | Department of Mathematics, Hangzhou Normal University, Hangzhou 310036,
China. | |
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| 中文摘要: |
| 给出了一类连分数的对致的线形型的下界估计:设{an是给定的正整致列,a与β是y=f(s)=alx+/1 a2x+/1…anx+/1 …在两个不同的正整数点的值,k和l是不全为零的整数,则存在常数c4,c6,使得|A|=|klog a+flog βI>c6exp(-c4Alog H),其中A=max{λ(μ(1ogH+1)+1),λ(μlogH+1)+2)}. |
| 英文摘要: |
| The lower bound of the
linear form of logarithms of a class of continued fractions was
given. Let $\{a_{n}\}$ be a given sequence of positive integers,
$\alpha$ and $\beta$ be the values of
$y=f(x)=\frac{1}{a_{1}x+}\frac{1}{a_{2}x+}\cdots\frac{1}{a_{n}x+}\cdots$
at two different positive integers respectively, $k$ and $l$ be
different integers. Then there exist constants $c_{4}$, $c_{6}$, such
that
$$
\begin{array}{ll}
|\Lambda|=|k\log{\alpha}+l\log{\beta}|>c_{6}\exp(-c_{4}A\log{H}),
\end{array}
$$
where
$A=\max{\{\lambda(\mu^{*}(\log{H}+1)+1),\lambda(\mu^{*}(\log{H}+1)+2)
}$\}. |
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