Orthogonal splitting and class numbers of quadratic forms |
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Authors: | Larry J Gerstein |
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Institution: | Department of Mathematics, University of California, Santa Barbara, California 93106 USA |
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Abstract: | Orthogonal splitting for lattices on quadratic spaces over algebraic number fields is studied. It is seen that if the rank of a lattice is sufficiently large, then its spinor genus must contain a decomposable lattice. Also, splitting theory is used to obtain a lower bound for the class number of a lattice (in the definite case) in terms of its rank, via the partition function. |
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