Positive definite unimodular lattices with trivial automorphism groups
Author(s)
Bibliographic Information
Positive definite unimodular lattices with trivial automorphism groups
（Memoirs of the American Mathematical Society, no. 429）
American Mathematical Society, 1990
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Note
"May 1990, volume 85, number 429 (second of 3 numbers)" -- T.p
Includes bibliographical references
Description and Table of Contents
Description
In this book the author proves that there exists a lattice with trivial automorphism group in every genus of positive definite unimodular Z-lattices of rank m (with m greater than or equal to 43 for the odd unimodular case and m greater than or equal to 144 for the even unimodular case). Siegel's mass formulas for lattices (for both orthogonal and hermitian cases) are used in the proof. In addition, the author shows that, for those positive definite unimodular Z-lattices in the given genus and of rank m, the ratio of the mass of classes approaches 0 very rapidly as m increases. The book is intended for researchers and advanced graduate students in the areas of number theory and quadratic forms.
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