Sara Chari , Sergio Ricardo Zapata Ceballos , Erik Holmes , Fatemeh Jalalvand , Rahinatou Yuh Njah Nchiwo , Kelly O'Connor , Fabian Ramirez , Sameera Vemulapalli
{"title":"签名为(2,1)的d4 -四次数域的单位格","authors":"Sara Chari , Sergio Ricardo Zapata Ceballos , Erik Holmes , Fatemeh Jalalvand , Rahinatou Yuh Njah Nchiwo , Kelly O'Connor , Fabian Ramirez , Sameera Vemulapalli","doi":"10.1016/j.jnt.2025.09.003","DOIUrl":null,"url":null,"abstract":"<div><div>There has been a recent surge of interest on distributions of shapes of unit lattices in number fields, due to both their applications to number theory and the lack of known results.</div><div>In this work we focus on <span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-quartic fields with signature <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>; such fields have a rank 2 unit group. Viewing the unit lattice as a point of <span><math><msub><mrow><mi>GL</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>Z</mi><mo>)</mo><mo>﹨</mo><mi>h</mi></math></span>, we prove that every lattice which arises this way must correspond to a transcendental point on the boundary of a certain fundamental domain of <span><math><msub><mrow><mi>GL</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>Z</mi><mo>)</mo><mo>﹨</mo><mi>h</mi></math></span>. Moreover, we produce three explicit (algebraic) points of <span><math><msub><mrow><mi>GL</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>Z</mi><mo>)</mo><mo>﹨</mo><mi>h</mi></math></span> which are limit points of the set of (points associated to) unit lattices of <span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-quartic fields with signature <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>.</div></div>","PeriodicalId":50110,"journal":{"name":"Journal of Number Theory","volume":"280 ","pages":"Pages 761-784"},"PeriodicalIF":0.7000,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Unit lattices of D4-quartic number fields with signature (2,1)\",\"authors\":\"Sara Chari , Sergio Ricardo Zapata Ceballos , Erik Holmes , Fatemeh Jalalvand , Rahinatou Yuh Njah Nchiwo , Kelly O'Connor , Fabian Ramirez , Sameera Vemulapalli\",\"doi\":\"10.1016/j.jnt.2025.09.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>There has been a recent surge of interest on distributions of shapes of unit lattices in number fields, due to both their applications to number theory and the lack of known results.</div><div>In this work we focus on <span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-quartic fields with signature <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>; such fields have a rank 2 unit group. Viewing the unit lattice as a point of <span><math><msub><mrow><mi>GL</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>Z</mi><mo>)</mo><mo>﹨</mo><mi>h</mi></math></span>, we prove that every lattice which arises this way must correspond to a transcendental point on the boundary of a certain fundamental domain of <span><math><msub><mrow><mi>GL</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>Z</mi><mo>)</mo><mo>﹨</mo><mi>h</mi></math></span>. Moreover, we produce three explicit (algebraic) points of <span><math><msub><mrow><mi>GL</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>Z</mi><mo>)</mo><mo>﹨</mo><mi>h</mi></math></span> which are limit points of the set of (points associated to) unit lattices of <span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span>-quartic fields with signature <span><math><mo>(</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>.</div></div>\",\"PeriodicalId\":50110,\"journal\":{\"name\":\"Journal of Number Theory\",\"volume\":\"280 \",\"pages\":\"Pages 761-784\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-10-01\",\"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/S0022314X25002562\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Number Theory","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022314X25002562","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Unit lattices of D4-quartic number fields with signature (2,1)
There has been a recent surge of interest on distributions of shapes of unit lattices in number fields, due to both their applications to number theory and the lack of known results.
In this work we focus on -quartic fields with signature ; such fields have a rank 2 unit group. Viewing the unit lattice as a point of , we prove that every lattice which arises this way must correspond to a transcendental point on the boundary of a certain fundamental domain of . Moreover, we produce three explicit (algebraic) points of which are limit points of the set of (points associated to) unit lattices of -quartic fields with signature .
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.