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| 对Baker~[1]-Mahler~[2]一个定理的注记 | |
| 引用本文： | 於坤瑞,徐广善. 对Baker~[1]-Mahler~[2]一个定理的注记[J]. 数学学报, 1979, 22(4): 487-494. DOI: cnki:ISSN:0583-1431.0.1979-04-007 |
| 作者姓名： | 於坤瑞 徐广善 |
| 作者单位： | 中国科学院数学研究所(於坤瑞)，中国科学院数学研究所(徐广善) |
| 摘 要： | <正> 对任意实数x,定义‖x‖=max(x-[x],[x]+1-x).设a_1,…,a_(k-1)是互不相等的非零整数,a是适合(a,a_1,…,a_(k-1)=1的正整数,r是正整数.置 |
| 收稿时间： | 1977-08-05 |
A NOTE ON A THEOREM OF BAKER-MAHLER |
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| Affiliation: | Yu Kunrui Xu Guangshan(Institute of Mathematics, Academia Sinica) |
| Abstract: | Let k ≥ 3 and a_1,…, a_(k-1) be distinct non-vanishing integers. Let a be a positive integer such that (a, a_1,…, a_(k-1)) = 1. Further, let B = a + max(|a_1|, …,|a_(k-1)|) and E_i = e~(ai/a)( 1≤i≤k - 1).We haveTheorem. Suppose that y ≥B~(16k4)·B~(16k4) Then we have y‖yE_1‖…‖yE_(k-1)‖>y~(-12k2(k+1)(log B·(log log y)-1))1/2(1)This gives a slight modification of a theorem due to Mahler, whose original result was obtained by replacing the right-hand side of (1) with y~(-12k3(k-1) (log B·(log log y)-1)1/2 |
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