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Representations of Integers as Sums of Squares

  • Emil Grosswald

Table of contents

  1. Front Matter
    Pages i-xi
  2. Emil Grosswald
    Pages 1-4
  3. Emil Grosswald
    Pages 5-12
  4. Emil Grosswald
    Pages 13-23
  5. Emil Grosswald
    Pages 38-65
  6. Emil Grosswald
    Pages 66-71
  7. Emil Grosswald
    Pages 91-106
  8. Emil Grosswald
    Pages 149-174
  9. Emil Grosswald
    Pages 175-187
  10. Emil Grosswald
    Pages 188-218
  11. Back Matter
    Pages 219-251

About this book

Introduction

During the academic year 1980-1981 I was teaching at the Technion-the Israeli Institute of Technology-in Haifa. The audience was small, but con­ sisted of particularly gifted and eager listeners; unfortunately, their back­ ground varied widely. What could one offer such an audience, so as to do justice to all of them? I decided to discuss representations of natural integers as sums of squares, starting on the most elementary level, but with the inten­ tion of pushing ahead as far as possible in some of the different directions that offered themselves (quadratic forms, theory of genera, generalizations and modern developments, etc.), according to the interests of the audience. A few weeks after the start of the academic year I received a letter from Professor Gian-Carlo Rota, with the suggestion that I submit a manuscript for the Encyclopedia of Mathematical Sciences under his editorship. I answered that I did not have a ready manuscript to offer, but that I could use my notes on representations of integers by sums of squares as the basis for one. Indeed, about that time I had already started thinking about the possibility of such a book and had, in fact, quite precise ideas about the kind of book I wanted it to be.

Keywords

DEX Farey sequence algebra algebraic number field classification computation development evaluation function functions number theory presentation theorem theta function time

Authors and affiliations

  • Emil Grosswald
    • 1
  1. 1.College of Liberal ArtsTemple UniversityPhiladelphiaUSA

Bibliographic information