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Pt. I. Arithmetic of ternary quadratic forms. Quadratic forms in n variables -- Introduction to ternary quadratic forms; universal forms -- Representation of binary forms by ternary forms -- Equivalence of indefinite, ternary, quadratic forms -- Genera and representation of numbers -- Quadratic Diophantine equations -- pt. II. Minima of indefinite quadratic forms. Minima of indefinite, binary quadratic forms -- Minima of indefinite, ternary, quadratic forms -- Minima of indefinite, quaternary, quadratic forms -- Tabulation of reduced, integral, ternary, quadratic forms which are indefinite, but not zero forms -- pt. III. Miscellaneous investigations of quadratic forms. Reduced, positive, quadratic forms; their minima -- Universal, zero, quadratic forms -- Number of representations as a sum of 5, 6, 7, or 8 squares.
This book covers topics including the Redei-Reichardt theorem, automorphs of ternary quadratic forms, facts concerning rational matrices leading to integral ternary forms representing zero, characteristics polynomials of symmetric matrices, and Gauss' theory of ternary quadratic forms.