Synopses & Reviews
The three-volume series
History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This final volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to quadratic and higher forms. It can be read independently of the preceding volumes, which explore divisibility and primality and diophantine analysis.
Topics include reduction and equivalence of binary quadratic forms and representation of integers; composition of binary quadratic forms; the composition of orders and genera; irregular determinants; classes of binary quadratic forms with integral coefficients; binary quadratic forms whose coefficients are complete integers or integers of a field; classes of binary quadratic forms with complex integral coefficients; ternary and quaternary quadratic forms; cubic forms in three or more variables; binary hermitian forms; bilinear forms, matrices, and linear substitutions; congruencial theory of forms; and many other related topics. Indexes of authors cited and subjects appear at the end of the book.
Synopsis
This third volume in the series
History of the Theory of Numbers presents nineteen chapters of material related to Quadratic and Higher Forms. Volume III is mainly concerned with general theories rather than with special problems and special theorems. The investigations deal with the most advanced parts of the theory of numbers. At the end of the volume is a separate subject and author index. Volume I: Divisibility and Primality (0-486-44232-2)and Volume II: Diophantine Analysis (0-486-44233-0) complete the three-volume set. Accessible and well-indexed, the three books survey the works of leading experts and can be used independently of each other.
Suitable for upper-level undergraduates and graduate students, this series is the work of a distinguished mathematician who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory.
Synopsis
This 3rd volume in the series History of the Theory of Numbers presents material related to Quadratic and Higher Forms. Volume III is mainly concerned with general theories rather than with special problems and special theorems. The investigations deal with the most advanced parts of the theory of numbers. 1919 edition.
About the Author
Leonard Eugene Dickson taught at the University of Chicago.
Table of Contents
I. Reduction and Equivalence of Binary Quadratic Forms, Representation of Integers
II. Explicit Values of x, y
III. Composition of Binary Quadratic Forms
IV. Orders and Genera; Their Composition
V. Irregular Determinants
VI. Number of Classes of Binary Quadratic Forms With Integral Coefficients
VII. Binary Quadratic Forms Whose Coefficients Are Complete Integers or Integers of a Field
VIII. Number of Classes of Binary Quadratic Forms with Complex Integral Coefficients
IX. Ternary Quadratic Forms
X. Quaternary Quadratic Forms
XI. Quadratic Forms in n Variables
XII. Binary Cubic Forms
XIII. Cubic Forms in Three or More Variables
XIV. Forms of Degree n>4
XV. Binary Hermitian Forms
XVI. Hermitian Forms in n Variables and Their Conjugates
XVII. Bilinear Forms, Matrices, Linear Substitutions
XVIII. Representation by Polynomials Modulo p
XIX. Congruencial Theory of Forms
Indexes