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Hurwitz's lectures on the number theory of quaternions /

Quaternions are non-commutative generalizations of the complex numbers, invented by William Rowan Hamilton in 1843. Their number-theoretical aspects were first investigated by Rudolf Lipschitz in the 1880s, and, in a streamlined form, by Adolf Hurwitz in 1896. This book contains an English translati...

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Bibliographic Details
Main Authors: Oswald, Nicola (Author), Steuding, Jörn (Author)
Format: Book
Language:English
Published: Berlin, Germany : EMS Press, 2023.
Series:Heritage of European mathematics.
Subjects:
Hurwitz, Adolf, > 1859-1919. > Works. > Selections.
Quaternions.
Number theory.
Table of Contents:
  • Introduction
  • Lectures on the number theory of quaternions
  • Preface
  • The quaternions and how to compute with them
  • The field of quaternions and their permutations and inversions
  • The field R and its permutations
  • The integer quaternions
  • The permutations of integer quaternions
  • Greatest common divisor and quaternion ideals
  • Even and odd quaternions. Associated and primary quaternions
  • The integer quaternions modulo an odd number
  • The prime quaternions
  • The factorization theorem
  • The representations of a positive integer as a sum of four squares
  • A problem due to Euler
  • Notes and addendum
  • Two Arithmetics
  • A view into Hurwitz's Mathematische Tagebücher
  • On the composition of quadratic forms
  • Abstraction and generalization
  • Epilogue
  • Appendix A: Theses
  • Appendix B: Elementary number theory in a nutshell.