East Asian mathematical journal

  • 제28권3호
  • /
  • Pages.333-337
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  • 2012
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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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)
  • 투고 : 2012.02.02
  • 심사 : 2012.04.11
  • 발행 : 2012.05.31
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초록

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.

키워드

참고문헌

  1. 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. https://doi.org/10.1142/S1793042107001103
  2. W. K. Chan, A. Rokicki, Positive definite binary Hermitian forms with finitely many exceptions, J. Number Theory 124 (2007), 167-180. https://doi.org/10.1016/j.jnt.2006.07.016
  3. W. K. Chan, A. G. Earnest, B.-K. Oh, Regularity properties of positive definite integral quadratic forms, Contemp. Math., 344 (2004), 59-71. https://doi.org/10.1090/conm/344/06208
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  8. H. Iwabuchi, Universal binary positive definite Hermitian lattices, Rocky Mountain J. Math. 30 (2000), 951-959. https://doi.org/10.1216/rmjm/1021477254
  9. 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. https://doi.org/10.2969/jmsj/06331001
  10. B.M. Kim, J.Y. Kim, P.-S.Park, Even universal binary Hermitian lattices over imaginary quadratic fields. Forum Math. 23 (2011), 1189-1201.
  11. B. M. Kim, P.-S. Park, Hermitian lattices without a basis of minimal vectors, Proc. Amer. Math. Soc. 136 (2008), 3041-3044.
  12. J.-H. Kim, P.-S. Park, A few uncaught universal Hermitian forms, Proc. of Amer. Math. Soc. 135 (2007), 47-49.
  13. O. T. O'Meara, Introduction to Quadratic Forms, Spinger-Verlag, New York, 1973.
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피인용 문헌

  1. Strictly regular ternary Hermitian forms vol.168, pp.None, 2016, https://doi.org/10.1016/j.jnt.2016.04.012