논문KCI 등재
Universal Quaternary Lattices over F_q[x]
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초록
In this paper, we show that any definite lattice over F_q[x] is universal if and only if it is quaternary and its discriminant is of degree 2, where ch(F_q)≠ 2. The Four Conjecture follows as an immediate consequence.
Abstract
In this paper, we show that any definite lattice over F_q[x] is universal if and only if it is quaternary and its discriminant is of degree 2, where ch(F_q)≠ 2. The Four Conjecture follows as an immediate consequence.
참고문헌 (9)
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- Kitaoka, Yoshiyuki, "Arithmetic of quadratic forms, Cambridge Tracts in Mathematics106" (1993), Cambridge University Press
- Kim, Myung-Hwan, "Recent developments on universal forms, Algebraic and arithmetic theory of quadratic forms", Contemp. Math, 215, pp.344~ (2004)
- Kim, Byeong Moon, "Oh, Byeong-Kweon, A niteness theorem for representability of quadratic forms by forms", J. Reine Angew. Math, 581, pp.23~30 (2005)
- 김명환, "Universal quadratic forms over polynomial rings", 대한수학회지, 45(5), pp.1311~1322 (2008), 대한수학회
- O'Meara, O. T., "The integral representations of quadratic forms over local elds", Amer. J. Math, 80, pp.843~878 (1958)
- O'Meara, O. T., "Introduction to quadratic forms, Reprint of the 1973 edition, Classics in Mathematics" (2000), Springer-Verlag
- "Proc. Amer. Math. Soc", 2005, 3121~3131
관련 논문AI추천
FINITENESS THEOREMS FOR 2-UNIVERSAL HERMITIAN LATTICES OVER SOME IMAGINARY QUADRATIC FIELDS박부성영남수학회 · East Asian Mathematical Journal2010 · 제26권 제5호Universal quadratic forms over polynomial rings김명환, Fei Xu, Yuanhua Wang대한수학회 · 대한수학회지2008 · 제45권 제5호Infinitely 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 제3호Primitive even 2-regular positive quaternary quadratic forms오병권대한수학회 · 대한수학회지2008 · 제45권 제3호Class number divisibility of quadratic function fields in even characteristic배성한, 정환엽대한수학회 · 대한수학회보2013 · 제50권 제4호
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