Book:Leonard Eugene Dickson/History of the Theory of Numbers/Volume III

Subject Matter

 * Number Theory

Contents

 * PREFACE


 * $\text{I}$. Reduction and Equivalence of Binary Quadratic Forms, Representation of Integers
 * $\text{II}$. Explicit Values of $x, y$ in $x^2 + \Delta y^2 = g$
 * $\text{III}$. Composition of Binary Quadratic Forms
 * $\text{IV}$. Orders and Genera: Their Composition
 * $\text{V}$. Irregular Determinants
 * $\text{VI}$. Number of Classes of Binary Quadratic Forms with Integral Coefficients
 * $\text{VII}$. Binary Quadratic Forms Whose Coefficients are Complex Integers or Integers of a Field
 * $\text{VIII}$. Number of Classes of Binary Quadratic Forms with Complex Integral Coefficients
 * $\text{IX}$. Ternary Quadratic Forms
 * $\text{X}$. Quaternary Quadratic Forms
 * $\text{XI}$. Quadratic Forms in $n$ Variables
 * $\text{XII}$. Binary Cubic Forms
 * $\text{XIII}$. Cubic Forms in Three or More Variables
 * $\text{XIV}$. Forms of Degree $n \ge 4$
 * $\text{XV}$. Binary Hermitian Forms
 * $\text{XVI}$. Hermitian Forms in $n$ Variaables and Their Conjugates
 * $\text{XVII}$. Bilinear Forms, Matrices, Linear Substitutions
 * $\text{XVIII}$. Representation by Polynomials Modulo $p$
 * Analytic Representation of Substitutions, Polynomials Representing All Integers Modulo $p$
 * Polynomials Representing Only Numbers of Prescribed Nature
 * $\text{XIX}$. Congruencial Theory of Forms
 * Modular Invariants and Covariants
 * Reduction of Modular Forms to Canonical Types
 * Formal Modular Invariants and Covariants
 * Formal Modular Invariants and Covariants


 * Author Index
 * Subject Index