Dihedral Artin representations and CM fields

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-02-07 DOI:10.1090/proc/16793

David Rohrlich

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引用次数: 0

Abstract

For a fixed CM field K K with maximal totally real subfield F F , we consider isomorphism classes of dihedral Artin representations of F F which are induced from K K , distinguishing between those which are “canonically” induced from K K and those which are “noncanonically” induced from K K . The latter can arise only for Artin representations with image isomorphic to the dihedral group of order 8. We show that asymptotically, the number of noncanonically induced isomorphism classes is always comparable to and in some cases exceeds the number of canonically induced ones.

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二面阿廷表示和 CM 场

对于具有最大全实子场 F F 的固定 CM 场 K K，我们考虑从 K K 诱导的 F F 的二面体阿廷表示的同构类，区分 "规范地 "从 K K 诱导的同构类和 "非规范地 "从 K K 诱导的同构类。后者只适用于其图像与 8 阶二面群同构的 Artin 表示。我们证明，从渐近的角度看，非规范诱导同构类的数量总是与规范诱导同构类的数量相当，在某些情况下甚至超过规范诱导同构类的数量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.