A Primer of Analytic Number Theory
eBook - PDF

A Primer of Analytic Number Theory

From Pythagoras to Riemann

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

A Primer of Analytic Number Theory

From Pythagoras to Riemann

Book details
Table of contents
Citations

About This Book

This 2003 undergraduate introduction to analytic number theory develops analytic skills in the course of studying ancient questions on polygonal numbers, perfect numbers and amicable pairs. The question of how the primes are distributed amongst all the integers is central in analytic number theory. This distribution is determined by the Riemann zeta function, and Riemann's work shows how it is connected to the zeroes of his function, and the significance of the Riemann Hypothesis. Starting from a traditional calculus course and assuming no complex analysis, the author develops the basic ideas of elementary number theory. The text is supplemented by series of exercises to further develop the concepts, and includes brief sketches of more advanced ideas, to present contemporary research problems at a level suitable for undergraduates. In addition to proofs, both rigorous and heuristic, the book includes extensive graphics and tables to make analytic concepts as concrete as possible.

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Yes, you can access A Primer of Analytic Number Theory by Jeffrey Stopple in PDF and/or ePUB format, as well as other popular books in Mathematics & Number Theory. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Cambridge University Press
Year
2003
ISBN
9780511058370
Topic
Mathematics
Subtopic
Number Theory
Index
Mathematics

Table of contents

  1. Cover
  2. Half-title
  3. Title
  4. Copyright
  5. Dedication
  6. Contents
  7. Preface
  8. Chapter 1 Sums and Differences
  9. Chapter 2 Products and Divisibility
  10. Chapter 3 Order of Magnitude
  11. Chapter 4 Averages
  12. Interlude 1 Calculus
  13. Chapter 5 Primes
  14. Interlude 2 Series
  15. Chapter 6 Basel Problem
  16. Chapter 7 Euler’s Product
  17. Interlude 3 Complex Numbers
  18. Chapter 8 The Riemann Zeta Function
  19. Chapter 9 Symmetry
  20. Chapter 10 Explicit Formula
  21. Interlude 4 Modular Arithmetic
  22. Chapter 11 Pell’s Equation
  23. Chapter 12 Elliptic Curves
  24. Chapter 13 Analytic Theory of Algebraic Numbers
  25. Solutions
  26. Bibliography
  27. Index