On Invariants and the Theory of Numbers

On Invariants and the Theory of Numbers

Author: Leonard Eugene Dickson

Publisher: Courier Corporation

Published: 2004-01-01

Total Pages: 128

ISBN-13: 9780486438283

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Of enormous historical importance, this classic offered the first public formulation of Dickson's theory of invariants for modular forms and linear transformations. In many sections of the five lectures included here, Dickson aimed not at complete generality, but at an illumination of typical and suggestive topics. The introductory lecture is followed by sections on seminvariants of algebraic and modular binary forms; invariants of a modular group and formal invariants and covariants of modular forms; modular geometry and covariantive theory of a quadratic form in m variables, modulo 2; and a theory of plane cubic curves with a real inflexion point valid in ordinary and in modular geometry. 1914 ed.


The Classical Groups

The Classical Groups

Author: Hermann Weyl

Publisher: Princeton University Press

Published: 1946

Total Pages: 338

ISBN-13: 9780691057569

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The author discusses symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are important in understanding the group-theoretic structure of quantum mechanics.