GL 2 (O K )-INVARIANT LATTICES IN THE SPACE OF BINARY CUBIC FORMS WITH COEFFICIENTS IN THE NUMBER FIELD K
In 2008, Ohno, Taniguchi and Wakatsuki obtained a classification of all GL 2 (ℤ)-invariant lattices in the space of binary cubic forms with coefficients in ℚ. In this paper, we aim to generalize their result by replacing the rational field with an arbitrary algebraic number field, K. We conclude the...
Saved in:
| Published in: | Proceedings of the American Mathematical Society Vol. 142; no. 7; pp. 2313 - 2325 |
|---|---|
| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
AMERICAN MATHEMATICAL SOCIETY
01-07-2014
|
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | In 2008, Ohno, Taniguchi and Wakatsuki obtained a classification of all GL
2
(ℤ)-invariant lattices in the space of binary cubic forms with coefficients in ℚ. In this paper, we aim to generalize their result by replacing the rational field with an arbitrary algebraic number field, K. We conclude the paper by connecting the lattices described in our main result to a zeta function developed by Datskovsky and Wright, which yields a functional equation for certain Dirichlet series attached to the lattices. |
|---|---|
| AbstractList | In 2008, Ohno, Taniguchi and Wakatsuki obtained a classification of all GL
2
(ℤ)-invariant lattices in the space of binary cubic forms with coefficients in ℚ. In this paper, we aim to generalize their result by replacing the rational field with an arbitrary algebraic number field, K. We conclude the paper by connecting the lattices described in our main result to a zeta function developed by Datskovsky and Wright, which yields a functional equation for certain Dirichlet series attached to the lattices. |
| Author | OSBORNE, CHARLES A. |
| Author_xml | – sequence: 1 givenname: CHARLES A. surname: OSBORNE fullname: OSBORNE, CHARLES A. |
| BookMark | eNqFi7sKwjAUQIMoWB-fINxRh0JM1TZjGhN7aU2ljYpTcVBo8UXr4t_rIK5Oh8Ph9Ej7dr-dWsSZ0iBwFwFbtIlDKWUu5x7vkl7TVB-d8pnvkHKVAINxCjFMXDQ7kaEwFhJhLUqVAxqwkYJ8I6SCVEOIRmQHkNsQJeg0W-ewRxuBTJXWKFEZ-5vMdh2qDDSqZAnxgHTOx0tzGn7ZJyOtrIzcqnne6-JRl9dj_SqYF1A-95n3r78BmO07CQ |
| ContentType | Journal Article |
| Copyright | 2014 American Mathematical Society |
| Copyright_xml | – notice: 2014 American Mathematical Society |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1088-6826 |
| EndPage | 2325 |
| ExternalDocumentID | 23809572 |
| GroupedDBID | -DZ -~X 123 2AX 2WC 4.4 85S 87J AAFVP ABBHK ABCQX ABFAN ABPFR ABPIV ABPPZ ABWJQ ABXSQ ABYAD ABYWD ACCNN ACMTB ACNCT ACTMH ACTWD ACUBG ADODI ADULT AENEX AEUPB AFVYC AFXHP AFXKK AIHXQ ALMA_UNASSIGNED_HOLDINGS CS3 D0L DQDLB DSRWC DU5 E3Z EBS ECEWR EFSUC EJD F20 HQ6 JAAYA JAS JBMMH JBZCM JENOY JHFFW JKQEH JLEZI JLXEF JMS JPL JSODD JST L7B MVM OK1 P2P RMA SA0 TN5 VQA WH7 X7L YNT |
| ID | FETCH-jstor_primary_238095723 |
| IEDL.DBID | JAS |
| ISSN | 0002-9939 |
| IngestDate | Fri Feb 02 08:05:19 EST 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 7 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-jstor_primary_238095723 |
| ParticipantIDs | jstor_primary_23809572 |
| PublicationCentury | 2000 |
| PublicationDate | 20140701 |
| PublicationDateYYYYMMDD | 2014-07-01 |
| PublicationDate_xml | – month: 7 year: 2014 text: 20140701 day: 1 |
| PublicationDecade | 2010 |
| PublicationTitle | Proceedings of the American Mathematical Society |
| PublicationYear | 2014 |
| Publisher | AMERICAN MATHEMATICAL SOCIETY |
| Publisher_xml | – name: AMERICAN MATHEMATICAL SOCIETY |
| SSID | ssj0001947 |
| Score | 4.1381397 |
| Snippet | In 2008, Ohno, Taniguchi and Wakatsuki obtained a classification of all GL
2
(ℤ)-invariant lattices in the space of binary cubic forms with coefficients in ℚ.... |
| SourceID | jstor |
| SourceType | Publisher |
| StartPage | 2313 |
| SubjectTerms | Algebra Coefficients Coordinate systems Cubic functions Discriminants Integers Mathematical functions Mathematical lattices Mathematical rings Numbers |
| Title | GL 2 (O K )-INVARIANT LATTICES IN THE SPACE OF BINARY CUBIC FORMS WITH COEFFICIENTS IN THE NUMBER FIELD K |
| URI | https://www.jstor.org/stable/23809572 |
| Volume | 142 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV07T8MwED7RTjDwrngV3QASDBGlSZMwuqlDrCYpalweU1UTR0JCAVH6_7kkJAMCidWW7ZPO8n1nf_cZ4Exn2SC1CuVHfWMbxReFhjJVz3B6i5SaTNMyi0LhIHHiR3fEC5mc87oWpqBVlrzA8hWfAJJ61VcUVggJOHTStii-VCq4zXFLWbhTY1wKtj-IhWWY8Lf-ucA2bH7jQGSV43ZgTee7sBE1IqrLPXi5DbGPFxMc46Uh4ns2FSyWGDIphccTFDHKgGNyxzyOEx-HImbTJ_RmQ-EhJXdRgg9CBuhNCIyK4jJJNoPiWTTkU_QFD0c43oeuz6UXGKXJ8_dKgWJe22t2oJ2_5foA0M3UYNB_1rambZ8tLGW5aZYSGunZ6tox1SF0fp_j6K-OY1gndGBV3NQTaH9-rHQXWst0dVp64Avh5oA6 |
| link.rule.ids | 315,783,787,818,58027,58260 |
| linkProvider | JSTOR |
| linkToHtml | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwjV3JTsMwEB1BOQAH9oqtMAeQ4BBRmpVjkjrEauKixmU5VTVxJCRUEKX_zyShPSCQuNqyPdJYnjf2m2eAM10Udm6Vyo_6xjHKLwoNZaq24bbHOTWZpmWWhcJx5opHr8tKmZzzeS1MSauseIHVKz4BJPWqryisEBJw6aRdsT3Ko2od3MWBS3m4O0e5FG5_UAurQBFt_nOJLdj4RoLo167bhiU92YH1dCGjOt2Fl9sEO3jRxx5eGlzc-wPuC4mJLyUPWYZcoIwZZnd-yLAfYcCFP3jCcBjwECm9SzN84DLGsE9wlJfXSXIxSAzTgA0w4izpYm8PWhGTYWxUJo_eaw2K0dxeswmNydtE7wN6hbLtzrN2NG38Ymwpy8uLnPBI21HXrqkOoPn7HId_dZzCaizTZJRw0TuCNcIKVs1UPYbG58dMt2B5ms9OKm98Adwfg4s |
| linkToPdf | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1LTwIxEJ4oJkYPvokvdA4e5LBhYV94XJau27AUwhYfJ0LdbmJikIj8f2d3hYPRg9c2bSeZtPNN-81XgBudZU5q58qP-s418i8KDWUp0_DMaUpNlmVbeaFwlHjiqd1luUxOfVULk9MqC15g8YpPAEm96cY8zRoUWggNeHTabjkEic1SC3d96FIu7q2QLoXcH_TCIliE-_9Y5gD2vhEh-qULD2FDz45gt7-WU10cw-t9jC28HWAP6wYXD_6I-0Ji7EvJA5YgFygjhsnQDxgOQuxw4Y-eMRh3eICU5vUTfOQywmBAsJTn10pyPUiM-x02wpCzuIu9E6iFTAaRUZg9mZdaFJOVvVYVKrP3mT4FbGfKcVov2tW0AbKprex2mqWES0xXNT1LnUH19znO_-q4hu1hN5zEXPQuYIcgg10SVi-h8vmx1DXYXKTLq8IhX5IPhgg |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=GL+2+%28O+K+%29-INVARIANT+LATTICES+IN+THE+SPACE+OF+BINARY+CUBIC+FORMS+WITH+COEFFICIENTS+IN+THE+NUMBER+FIELD+K&rft.jtitle=Proceedings+of+the+American+Mathematical+Society&rft.au=OSBORNE%2C+CHARLES+A.&rft.date=2014-07-01&rft.pub=AMERICAN+MATHEMATICAL+SOCIETY&rft.issn=0002-9939&rft.eissn=1088-6826&rft.volume=142&rft.issue=7&rft.spage=2313&rft.epage=2325&rft.externalDocID=23809572 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0002-9939&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0002-9939&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0002-9939&client=summon |