Powerful values of polynomials and a conjecture of Vojta

JOURNAL OF NUMBER THEORY

卷:133

Article

Pasten, Hector

关键词: Squareful;    Powerful numbers;    Vojta's conjecture;    Buchi's problem;    Undecidability;   

DOI  :  10.1016/j.jnt.2013.03.001

来源: Elsevier

【 摘 要 】

We study some problems about powerful values of polynomials over number fields, such as giving uniform bounds for the number of consecutive squareful values of squarefree polynomials, or the higher exponent analogue of the M squares problem. We show that a Diophantine conjecture of Vojta implies complete answers to these problems, and we show unconditional analogues for function fields and complex meromorphic functions. Some of these results have consequences in logic related to Hilbert's tenth problem, and we also explore these. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free