History of the Theory of Numbers

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  • Format: Hardcover
  • Copyright: 1999-05-01
  • Publisher: Amer Mathematical Society

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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 under-graduates 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.

Table of Contents

Reduction and Equivalence of Binary Quadratic Forms, Representation of Integersp. 1
Explicit Values of x, y in x[superscript 2] + [Delta]y[superscript 2] = gp. 55
Composition of Binary Quadratic Formsp. 60
Orders and Genera; Their Compositionp. 80
Irregular Determinantsp. 89
Number of Classes of Binary Quadratic Forms with Integral Coefficientsp. 92
Binary Quadratic Forms Whose Coefficients Are Complex Integers or Integers of a Fieldp. 198
Number of Classes of Binary Quadratic Forms with Complex Integral Coefficientsp. 203
Ternary Quadratic Formsp. 206
Quaternary Quadratic Formsp. 225
Quadratic Forms in n Variablesp. 234
Binary Cubic Formsp. 253
Cubic Forms in Three or More Variablesp. 259
Forms of Degree n [greater than or equal] 4p. 262
Binary Hermitian Formsp. 269
Hermitian Forms in n Variables and Their Conjugatesp. 279
Bilinear Forms, Matrices, Linear Substitutionsp. 284
Representation by Polynomials Modulo pp. 289
Analytic Representation of Substitutions, Polynomials Representing All Integers Modulo pp. 289
Polynomials Representing Only Numbers of Prescribed Naturep. 291
Congruencial Theory of Formsp. 293
Modular Invariants and Covariantsp. 293
Reduction of Modular Forms to Canonical Typesp. 298
Formal Modular Invariants and Covariantsp. 299
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