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

Leonard Eugene Dickson: History of the Theory of Numbers, Volume $\text { III: Quadratic and Higher Forms }$

Published $\text {1923}$, AMS Chelsea

ISBN 0-8218-1936-4

Subject Matter

• Number Theory

Contents

PREFACE

Chapter.

$\text{I}$. 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

Author Index

Subject Index