论文标题
关于dirichlet $ l $ values的线性独立性
On linear independence of Dirichlet $L$ values
论文作者
论文摘要
对于固定整数$ k> 1 $和$χ$的线性独立性的研究$ l（k，χ）$的研究非常取决于$ k $ vis $ vis $χ$的均等。许多作者对固定模量的dirichlet字符$χ$进行了调查，并且具有与$ k $相同的平价。本文的焦点是将此调查扩展到Dirichlet字符的家族Modulo Modulo Differtwise Copime Prime自然数字。在固定模量的背景下，所得的环境数字字段之间的相互作用带来了迄今缺乏新的技术问题和并发症（因此，在后台潜伏了单个数字字段）。这需要一个非常谨慎和动手处理，以处理我们在这项工作中所承担的数字字段的算术。我们的结果扩展了第一作者的早期作者以及冈田，穆尔蒂·萨拉达和哈马哈塔的作品。
The study of linear independence of $L(k, χ)$ for a fixed integer $k>1$ and varying $χ$ depends critically on the parity of $k$ vis-à-vis $χ$. This has been investigated by a number of authors for Dirichlet characters $χ$ of a fixed modulus and having the same parity as $k$.The focal point of this article is to extend this investigation to families of Dirichlet characters modulo distinct pairwise co-prime natural numbers. The interplay between the resulting ambient number fields brings in new technical issues and complications hitherto absent in the context of a fixed modulus (consequently a single number field lurking in the background). This entails a very careful and hands-on dealing with the arithmetic of compositum of number fields which we undertake in this work. Our results extend earlier works of the first author with Murty-Rath as well as works of Okada, Murty-Saradha and Hamahata.
