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Primitive even 2-regular positive quaternary quadratic forms

오병권
대한수학회 (The Korean Mathematical Society)|2008.05|대한수학회지 (Journal of the KMS)|제45권 제3호|pp. 621-630

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참고문헌

키워드

2-regular quaternary quadratic forms
주제분류수학

초록

In this paper, we provide a complete list of 177 equivalence classes of primitive even 2-regular quaternary positive definite quadratic forms and their discriminants. All of them have class number 1.

Abstract

In this paper, we provide a complete list of 177 equivalence classes of primitive even 2-regular quaternary positive definite quadratic forms and their discriminants. All of them have class number 1.

참고문헌 (16)

  1. H. Brandt, "Tabellen reduzierter positiver ternarer quadratischer Formen", Abhandlungen der Sachsischen Akademie der Wissenschaften zu Leipzig. Mathematisch-Naturwissenschaftliche Klasse, 45(4), pp.261~ (1958)
  2. W. K. Chan, "Finiteness theorems for positive definite n-regular quadratic forms", Transactions of the American Mathematical Society, 355(6), pp.2385~2396 (2003)
  3. L. E. Dickson, "Ternary quadratic forms and congruences", Annals of Mathematics, 28(1), pp.333~341 (1926)
  4. A. G. Earnest, "The representation of binary quadratic forms by positive definite quaternary quadratic forms", Transactions of the American Mathematical Society, 345(2), pp.853~863 (1994)
  5. W. C. Jagy, "There are 913 regular ternary forms", Mathematika, 44(2), pp.332~341 (1997)
  6. B. W. Jones, "Regular and semi-regular positive ternary quadratic forms", Acta Mathematica, 70(1), pp.165~191 (1939)
  7. A. Khosravani, "Universal quadratic and Hermitian forms, Integral quadratic forms and lattices (Seoul, 1998)", Contemporary Mathematics, 249, pp.43~49 (1999)
  8. Y. Kitaoka, "Arithmetic of Quadratic Forms, Cambridge Tracts in Mathematics", pp.106~ (1993), Cambridge University Press
  9. G. Nipp, "Quaternary Quadratic Forms" (1991), Springer-Verlag
  10. O. T. OMeara, "The integral representations of quadratic forms over local fields", American Journal of Mathematics, 80, pp.843~878 (1958)
  11. O. T. OMeara, "Introduction to Quadratic Forms, Die Grundlehren der mathematischen Wissenschaften", pp.117~, Academic Press, Inc.
  12. B. L. van derWaerden, "Die Reduktionstheorie der positiven quadratischen Formen", Acta Mathematica, 96, pp.265~309 (1956)
  13. G.L.Watson,Some problems in the theory of numbers, "Some problems in the theory of numbers", 박사, pp.1953
  14. G. L. Watson, "The representation of integers by positive ternary quadratic forms", Mathematika, 1, pp.104~110 (1954)
  15. G. L. Watson, "Transformations of a quadratic form which do not increase the class-number", Proc. London Math. Soc., 통권 : 12, pp.577~587 (1962)
  16. G. L. Watson, "Regular positive ternary quadratic forms", Journal of the London Mathematical Society, 13(1), pp.97~102 (1976)

관련 논문AI추천

EVEN 2-UNIVERSAL QUADRATIC FORMS OF RANK 5김명재, 오병권, 지윤성대한수학회 · 대한수학회지2021 · 제58권 제4호Representations by quaternary quadratic forms with coefficients 1, 2, 5 or 10Ayse Alaca, Mada Altiary대한수학회 · 대한수학회논문집2019 · 제34권 제1호REPRESENTATIONS BY QUATERNARY QUADRATIC FORMS WITH COEFFICIENTS 1, 2, 11 AND 22Bulent Kokluce대한수학회 · 대한수학회보2023 · 제60권 제1호Representation numbers by quadratic forms of certain levels엄익선대한수학회 · 대한수학회지2024 · 제61권 제6호Infinitely many regular subnormal binary Hermitian lattices over imaginary quadratic fields김병문, 김지영, 박부성영남수학회 · East Asian Mathematical Journal2012 · 제28권 제3호Oh's 8-Universality Criterion is UniqueScott Duke Kominers경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2021 · 제61권 제3호

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