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Utilizing lattice theory , the following results are obtained: with arbitrary nature number n and d, there exist indecomposable positive integer Hermitian forms over Q(mi)(m≡3 (mod 4)) with rank n and discriminant d. But for several exception cases: Q(3i),n=2,d=1,2,4,10; n=3,d=1,2,5;n=4,d=1,2;n=5,d=1;n=7,d=1; Q(7i): n=2,d=1; Q(11i): n=2,d=2;n=3,d=1, there don′t exist the forms with above property.
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Basic Information:
China Classification Code:O156.5
Citation Information:
[1]Wang Ruiqing1 , Li Guosheng2 (1.Fundamental Board, Zhongyuan Institute of Technology, Zhengzhou 450007, 2.Department of Mathematics, Zhumadian Teacher College, Zhumadian Henan 463000).Indecomposable Definite Hermite Forms over Imaginary Quadratic Fields[J].Journal of Zhengzhou University(Natural Science Edition),2001(03):22-27.
2001-09-25
2001-09-25