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

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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


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