The fifteen theorem for universal Hermitian lattices over imaginary quadratic fields
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- by Byeong Moon Kim, Ji Young Kim and Poo-Sung Park PDF
- Math. Comp. 79 (2010), 1123-1144 Request permission
Abstract:
We will introduce a method to get all universal Hermitian lattices over imaginary quadratic fields $\mathbb {Q}(\sqrt {-m})$ for all $m$. For each imaginary quadratic field $\mathbb {Q}(\sqrt {-m})$, we obtain a criterion on universality of Hermitian lattices: if a Hermitian lattice $L$ represents 1, 2, 3, 5, 6, 7, 10, 13, 14 and 15, then $L$ is universal. We call this the fifteen theorem for universal Hermitian lattices. Note that the difference between Conway-Schneeberger’s fifteen theorem and ours is the number 13. In addition, we determine the minimal rank of universal Hermitian lattices for all imaginary quadratic fields.References
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Additional Information
- Byeong Moon Kim
- Affiliation: Department of Mathematics, Kangnung-Wonju National University, 123 Chibyondong, Gangneung, Gangwon-Do, Korea
- Email: kbm@nukw.ac.kr
- Ji Young Kim
- Affiliation: School of Mathematics, Korea Institute for Advanced Study, Hoegiro 87, Dongdaemun-gu, Seoul, 130-722, Korea
- ORCID: setImmediate$0.46123087575319377$2
- Email: jykim@kias.re.kr
- Poo-Sung Park
- Affiliation: Department of Mathematics Education, Kyungnam University, Masan, Kyungnam, 631-701, Korea
- Email: pspark@kyungnam.ac.kr
- Received by editor(s): March 28, 2008
- Received by editor(s) in revised form: April 14, 2009
- Published electronically: July 16, 2009
- Additional Notes: The first named author was supported by the Korean Council for University Education, grant funded by Korean Government (MOEHRD) for 2006 Domestic Faculty Exchange.
The second and the third named authors were partially supported by KRF(2005-070-c00004). - © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 79 (2010), 1123-1144
- MSC (2000): Primary 11E39; Secondary 11E20, 11E41
- DOI: https://doi.org/10.1090/S0025-5718-09-02287-X
- MathSciNet review: 2600559