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Quaternary Even Positive Definite Quadratic Forms of Discriminant 4p

โœ Scribed by Wai Kiu Chan

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
159 KB
Volume
76
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

Let p>13 be a prime congruent to 1 modulo 4. Let G be the genus of a quaternary even positive definite Z-lattice of discriminant 4p whose 2-adic localization has a proper 2-modular Jordan component. We show that the orthogonal group of any lattice from G is generated by &1 and the symmetries with respect to the roots of the lattice. The class number of G is computed. Furthermore, we show that the theta series of degree two coming from the classes in G with non-trivial automorphism groups are linearly independent.

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