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9780486442341

History of the Theory of Numbers, Volume III Quadratic and Higher Forms

by
  • ISBN13:

    9780486442341

  • ISBN10:

    0486442349

  • Format: Paperback
  • Copyright: 2005-06-03
  • Publisher: Dover Publications

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Summary

This 3rd volume in the seriesHistory of the Theory of Numberspresents 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.

Author Biography

Leonard Eugene Dickson taught at the University of Chicago.

Table of Contents

I. REDUCTION AND EQUIVALENCE OF BINARY QUADRATIC FORMS, REPRESENTATION OF INTEGERS 1(54)
II. EXPLICIT VALUES OF x, y IN x²+ Δy² = g 55(5)
III. COMPOSITION OF BINARY QUADRATIC FORMS 60(20)
IV. ORDERS AND GENERA; THEIR COMPOSITION 80(9)
V. IRREGULAR DETERMINANTS 89(3)
VI. NUMBER OF CLASSES OF BINARY QUADRATIC FORMS WITH INTEGRAL COEFFICIENTS 92(106)
VII. BINARY QUADRATIC FORMS WHOSE COEFFICIENTS ARE COMPLEX INTEGERS OR INTEGERS OF A FIELD 198(5)
VIII. NUMBER OF CLASSES OF BINARY QUADRATIC FORMS WITH COMPLEX INTEGRAL COEFFICIENTS 203(3)
IX. TERNARY QUADRATIC FORMS 206(19)
X. QUATERNARY QUADRATIC FORMS 225(9)
XI. QUADRATIC FORMS IN n VARIABLES 234(19)
XII. BINARY CUBIC FORMS 253(6)
XIII. CUBIC FORMS IN THREE OR MORE VARIABLES 259(3)
XIV. FORMS OF DEGREE n > or equal to 4 262(7)
XV. BINARY HERMITIAN FORMS 269(10)
XVI. HERMITIAN FORMS IN n VARIABLES AND THEIR CONJUGATES 279(5)
XVII. BILINEAR FORMS, MATRICES, LINEAR SUBSTITUTIONS 284(5)
XVIII. REPRESENTATION BY POLYNOMIALS MODULO p 289(4)
Analytic Representation of Substitutions, Polynomials Representing All Integers Modulo p
289(2)
Polynomials Representing Only Numbers of Prescribed Nature
291(2)
XIX. CONGRUENCIAL THEORY OF FORMS 293(10)
Modular Invariants and Covariants
293(5)
Reduction of Modular Forms to Canonical Types
298(1)
Formal Modular Invariants and Covariants
299(4)
AUTHOR INDEX 303(6)
SUBJECT INDEX 309

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