论文信息 - On positive definite hermitian forms

On positive definite hermitian forms

Kneser's method of constructing adjacent lattices will be used to determine class numbers of unimodular positive definite hermitian lattices of rank 2 and 3 over rings of integers in some imaginary quadratic fields.The same method will also be applied in order to construct indecomposable unimodular positive definite hermitian lattices of rank 2 and 3 over almost all orders in imaginary quadratic fields, even non-maximal ones. All exceptional cases will be determined explicitly.

D. Hoffmann | Detlev W. Hoffmann

[1] Jean-Pierre Serre,et al. Nombres de points des courbes algébriques sur F ... , 1983 .

[2] H. Bass,et al. TORSION FREE AND PROTECTIVE MODULES , 2010 .

[3] Walter Feit,et al. Some lattices over Q(√−3)☆ , 1978 .

[4] M. Kneser,et al. Klassenzahlen definiter quadratischer Formen , 1957 .

[5] G. Shimura,et al. ARITHMETIC OF UNITARY GROUPS , 1964 .

[6] Tsuyoshi Hayashida,et al. Existence of curves of genus two on a product of two elliptic curves , 1965 .

[7] Ronald Jacobowitz,et al. Hermitian Forms Over Local Fields , 1962 .

[8] INTEGRAL DECOMPOSITION OF HERMITIAN FORMS. , 1970 .

[9] O. O’Meara. Introduction to quadratic forms , 1965 .

[10] Walther Landherr. Äquivalenz Hermitescher Formen über einem beliebigen algebraischen Zahlkörper , 1935 .

[11] M. Kneser. Zur Theorie der Kristallgitter , 1954 .

[12] G. C. Shephard,et al. Finite Unitary Reflection Groups , 1954, Canadian Journal of Mathematics.

[13] Kenichi Iyanaga,et al. Class numbers of definite Hermitian forms , 1969 .

[14] The Construction of Definite Indecomposable Hermitian Forms , 1978 .

[15] H. Reichardt. O. T. O'Meara, Introduction to Quadratic Forms. (Die Grundlehren der math. Wiss., Band 117) XII + 342 S. m. 10 Fig. Berlin/Göttingen/Heidelberg 1963. Springer-Verlag. Preis geb. DM 48,– , 1966 .