论文标题
围绕贝克的问题
Around a question of Baker
论文作者
论文摘要
对于任何正整数$ Q $，这是面包师的问题，即$ l（1，χ）$（$χ$）在非平凡字符上运行的$ c $ mod $ q $是否在$ \ mathbb {q} $上是线性独立的。这个问题以肯定的素数回答，但对于任意模量而言是未知的。在此说明中，我们概述了这个问题的起源和历史以及最新的。我们还介绍了进入该主题的数学思想，并阐明了阻碍我们回答任意模量问题的障碍。我们还描述了这个问题的许多概括和扩展。
For any positive integer $q$, it is a question of Baker whether the numbers $L(1, χ)$, where $χ$ runs over the non-trivial characters mod $q$, are linearly independent over $\mathbb{Q}$. The question is answered in affirmative for primes but is unknown for an arbitrary modulus. In this expository note, we give an overview of the origin and history of this question as well as the state-of-the-art. We also give an account of the mathematical ideas that enter into this theme as well as elucidate the obstructions that preclude us from answering the question for arbitrary modulus. We also describe a number of generalizations and extensions of this question.
