Multiplicative dependence of rational values modulo approximate finitely generated groups

IF 0.6 3区 数学 Q3 MATHEMATICS
ATTILA BÉRCZES, YANN BUGEAUD, KÁLMÁN GYŐRY, JORGE MELLO, ALINA OSTAFE, MIN SHA
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引用次数: 0

Abstract

In this paper, we establish some finiteness results about the multiplicative dependence of rational values modulo sets which are ‘close’ (with respect to the Weil height) to division groups of finitely generated multiplicative groups of a number field K. For example, we show that under some conditions on rational functions Abstract Image$f_1, \ldots, f_n\in K(X)$, there are only finitely many elements Abstract Image$\alpha \in K$ such that Abstract Image$f_1(\alpha),\ldots,f_n(\alpha)$ are multiplicatively dependent modulo such sets.

有理值模近似有限生成群的乘法依赖性
在本文中,我们建立了一些关于有理值模数集乘法依赖性的有限性结果,这些有理值模数集 "接近"(关于魏尔高度)数域 K 的有限生成乘法群的除法群。例如,我们证明了在有理函数 $f_1,\ldots,f_n/in K(X)$ 的某些条件下,K$ 中只有有限多个元素 $alpha \inK$使得 $f_1(\alpha),\ldots,f_n(\alpha)$ 与这些集合具有乘法依赖性。
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来源期刊
CiteScore
1.70
自引率
0.00%
发文量
39
审稿时长
6-12 weeks
期刊介绍: Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.
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