{"title":"Log-free zero density estimates for automorphic L-functions","authors":"Chen An","doi":"10.1016/j.jnt.2024.03.012","DOIUrl":null,"url":null,"abstract":"<div><p>We prove a log-free zero density estimate for automorphic <em>L</em>-functions defined over a number field <em>k</em>. This work generalizes and sharpens the method of pseudo-characters and the large sieve used earlier by Kowalski and Michel. As applications, we demonstrate for a particular family of number fields of degree <em>n</em> over <em>k</em> (for any <em>n</em>) that an effective Chebotarev density theorem and a bound on <em>ℓ</em>-torsion in class groups hold for almost all fields in the family.</p></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Number Theory","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022314X2400088X","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove a log-free zero density estimate for automorphic L-functions defined over a number field k. This work generalizes and sharpens the method of pseudo-characters and the large sieve used earlier by Kowalski and Michel. As applications, we demonstrate for a particular family of number fields of degree n over k (for any n) that an effective Chebotarev density theorem and a bound on ℓ-torsion in class groups hold for almost all fields in the family.
我们证明了定义在数域 k 上的自变 L 函数的无对数零密度估计。这项工作推广并强化了科瓦尔斯基（Kowalski）和米歇尔（Michel）早先使用的伪字符和大筛方法。作为应用，我们证明了对于k上n度数域的一个特定族（对于任意n），有效的切博塔列夫密度定理和类群中的ℓ-torsion约束对于族中的几乎所有域都成立。
期刊介绍：
The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field.
The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory.
Starting in May 2019, JNT will have a new format with 3 sections:
JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access.
JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions.
Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.
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