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Hermitian lattices without a basis of minimal vectors

Author(s): Byeong Moon Kim; Poo-Sung Park
Journal: Proc. Amer. Math. Soc. 136 (2008), 3041-3044.
MSC (2000): Primary 11E39; Secondary 11H50
Posted: April 17, 2008
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Abstract: It is shown that over infinitely many imaginary quadratic fields there exists a Hermitian lattice in all even ranks $n \ge 2$ which is generated by its minimal vectors but which is not generated by minimal vectors.

References:

1.: J. H. Conway, N. J. A. Sloane, A lattice without a basis of minimal vectors. Mathematika 42 (1995), 175-177. MR 1346681 (96e:11089)
2.: P. Erdös, Arithmetical properties of polynomials. J. London Math. Soc. 28 (1953), 416-425. MR 0056635 (15:104f)
3.: B. M. Kim, Universal octonary diagonal forms over some real quadratic fields. Comment. Math. Helv. 75 (2000), 410-414. MR 1793795 (2001m:11046)

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Additional Information:

Byeong Moon Kim
Affiliation: Department of Mathematics, Kangnung National University, Kangnung, Korea
Email: kbm@kangnung.ac.kr

Poo-Sung Park
Affiliation: Korea Institute for Advanced Study, Cheongnyangni 2-dong, Dongdaemun-gu, Seoul, 130-722, Korea
Email: sung@kias.re.kr

DOI: 10.1090/S0002-9939-08-09326-X
PII: S 0002-9939(08)09326-X
Keywords: Hermitian lattice, minimal vector
Received by editor(s): July 6, 2007
Posted: April 17, 2008
Additional Notes: The second author was partially supported by KRF(2003-070-c00001)
Communicated by: Wen-Ching Winnie Li
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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