Hensleys problem for complex and non-Archimedean meromorphic functions

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• 作者：Ta Thi Hoai An^a ; ¹ ; ^{tthan@math.ac.vn"" rel=""nofollow} ; Julie Tzu-Yueh Wang^b ; ² ; ^{jwang@math.sinica.edu.tw"" rel=""nofollow}
• 关键词：Buchi ; //www.sciencedirect.com/scidirimg/entities/2bc.gif"" alt=""modifier letter apostrophe"" title=""modifier letter apostrophe"" border=""0"">s problem ; Hensley ; //www.sciencedirect.com/scidirimg/entities/2bc.gif"" alt=""modifier lette
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2011
• 出版时间：15 September 2011
• 年：2011
• 卷：381
• 期：2
• 页码：661-677
• 全文大小：238 K

文摘

Büchis problem asks if there exists a positive integer M such that all satisfying the equations for all 3rM must also satisfy for some integer x. Hensleys problem asks if there exists a positive integer M such that, for any integers ν and a, if (ν+r)²−a is a square for 1rM, then a=0. It is not difficult to see that a positive answer to Hensleys problem implies a positive answer to Büchis problem. One can ask a more general version of the Hensleys problem by replacing the square by n-th power for any integer n2 which is called the Hensleys n-th power problem. In this paper we will solve Hensleys n-th power problem for complex meromorphic functions and non-Archimedean meromorphic functions.