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http://dx.doi.org/10.7858/eamj.2012.28.3.333

INFINITELY MANY REGULAR SUBNORMAL BINARY HERMITIAN LATTICES OVER IMAGINARY QUADRATIC FIELDS

Kim, Byeong-Moon (Department of Mathematic Gangneung-Wonju National University)
Kim, Ji-Young (Department of Mathematical Sciences Seoul National University)
Park, Poo-Sung (Department of Mathematics Education Kyungnam University)

Publication Information

East Asian mathematical journal / v.28, no.3, 2012 , pp. 333-337 More about this Journal

Abstract

Finiteness of regular normal binary Hermitian lattices are known in several articles. In this article, we point out that there are infinitely many imaginary quadratic fields that admit a regular subnormal binary Hermitian lattice.

Keywords

Hermitian lattices; regular lattices;

Citations & Related Records

Reference

1	B. M. Kim, P.-S. Park, Hermitian lattices without a basis of minimal vectors, Proc. Amer. Math. Soc. 136 (2008), 3041-3044.
2	J.-H. Kim, P.-S. Park, A few uncaught universal Hermitian forms, Proc. of Amer. Math. Soc. 135 (2007), 47-49.
3	O. T. O'Meara, Introduction to Quadratic Forms, Spinger-Verlag, New York, 1973.
4	G. L. Watson, The representation of integers by positive ternary quadratic forms, Mathematika 1 (1954), 104-110. DOI
5	W. K. Chan, A. G. Earnest, M. I. Icaza, J. Y. Kim, Finiteness results for regular definite ternary quadratic forms over Q( $\sqrt{5}$ ), Int. J. Number Theory, 3 (2007), 541-556. DOI ScienceOn
6	W. K. Chan, A. Rokicki, Positive definite binary Hermitian forms with finitely many exceptions, J. Number Theory 124 (2007), 167-180. DOI ScienceOn
7	W. K. Chan, A. G. Earnest, B.-K. Oh, Regularity properties of positive definite integral quadratic forms, Contemp. Math., 344 (2004), 59-71. DOI
8	J. H. Conway, Universal quadratic forms and the fifteen theorem, Contemp. Math. 272 (2000), 23-26. DOI
9	L. E. Dickson, Ternary quadratic forms and congruences, Ann. of Math. 28 (1927), 331-341.
10	A. G. Earnest, A. Khosravani, Universal binary Hermitian forms, Math. Comp. 66 (1997), 1161-1168. DOI ScienceOn
11	A. G. Earnest, A. Khosravani, Representation of integers by positive definite binary Hermitian lattices over imaginary quadratic fields, J. Number Theory 62 (1997), 368-374. DOI ScienceOn
12	G. L. Watson, Some problems in the theory of numbers, Ph.D. thesis, University of London, 1953.
13	H. Iwabuchi, Universal binary positive definite Hermitian lattices, Rocky Mountain J. Math. 30 (2000), 951-959. DOI
14	B.M. Kim, J.Y. Kim, P.-S. Park, Complete classifiaction of binary normal regular Hermitian lattices over imaginary quadratic fields, J. Math. Soc. Japan 63 (2011), 1001-1025. DOI
15	B.M. Kim, J.Y. Kim, P.-S.Park, Even universal binary Hermitian lattices over imaginary quadratic fields. Forum Math. 23 (2011), 1189-1201.