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FINITENESS THEOREMS FOR 2-UNIVERSAL HERMITIAN LATTICES OVER SOME IMAGINARY QUADRATIC FIELDS

박부성
영남수학회 (Youngnam Mathematical Society)|2010.11|East Asian Mathematical Journal|제26권 제5호|pp. 649-654

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참고문헌

키워드

local representationHermitian forms2-universal
주제분류수학

초록

A positive definite Hermitian lattice is said to be 2-universal if it represents all positive definite binary Hermitian lattices. We find some finiteness theorems which ensure 2-universality of Hermitian lattices over several imaginary quadratic number fields.

Abstract

A positive definite Hermitian lattice is said to be 2-universal if it represents all positive definite binary Hermitian lattices. We find some finiteness theorems which ensure 2-universality of Hermitian lattices over several imaginary quadratic number fields.

참고문헌 (11)

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  3. L. J. Gerstein, "Interal decomposition of Hermitian forms", Amer. J. Math., 92, pp.398~418 (1970)
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  5. B. M. Kim, "A niteness theorem for representability of qua-dratic forms by forms", J. reine angew. Math., 581, pp.23~30 (2005)
  6. B. M. Kim, "The fteen theorem for Hermitian lattices over imaginary quadratic elds", Math. Comp., 79, pp.1123~1144 (2010)
  7. M.-H. Kim, "Recent developments on universal forms", Contemp. Math., 344, pp.215~228 (2004)
  8. M.-H. Kim, "2-universal Hermitian lattices over imaginary quadratic elds", Ramanujan J., 22, pp.139~151 (2010)
  9. O. T. O'Meara, "Introduction to Quadratic Forms" (1973), Spinger-Verlag
  10. G. Shimura, "Arithmetic of unitary groups", Ann. Math., 79, pp.369~409 (1964)
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