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Number Theory

  • R. P. Bambah
  • V. C. Dumir
  • R. J. Hans-Gill

Part of the Trends in Mathematics book series (TM)

Table of contents

  1. Front Matter
    Pages i-vii
  2. R. P. Bambah, V. C. Dumir, R. J. Hans-Gill
    Pages 15-41
  3. Paul T. Bateman, Harold G. Diamond
    Pages 43-54
  4. Jerzy Browkin
    Pages 75-105
  5. Edmund Hlawka
    Pages 141-155
  6. Erik Jensen, M. Ram Murty
    Pages 167-181
  7. Neal Koblitz
    Pages 217-239
  8. Dipendra Prasad, C. S. Yogananda
    Pages 301-314
  9. A. R. Rajwade
    Pages 325-349
  10. K. Ramachandra
    Pages 351-370
  11. R. A. Rankin
    Pages 371-399
  12. S. S. Ryshkov, R. G. Barykinskii, Y. V. Kucherinenko
    Pages 401-461

About this book

Introduction

The Indian National Science Academy on the occasion ofthe Golden Jubilee Celebration (Fifty years of India's Independence) decided to publish a number of monographs on the selected fields. The editorial board of INS A invited us to prepare a special monograph in Number Theory. In reponse to this assignment, we invited several eminent Number Theorists to contribute expository/research articles for this monograph on Number Theory. Al­ though some ofthose invited, due to other preoccupations-could not respond positively to our invitation, we did receive fairly encouraging response from many eminent and creative number theorists throughout the world. These articles are presented herewith in a logical order. We are grateful to all those mathematicians who have sent us their articles. We hope that this monograph will have a significant impact on further development in this subject. R. P. Bambah v. C. Dumir R. J. Hans-Gill A Centennial History of the Prime Number Theorem Tom M. Apostol The Prime Number Theorem Among the thousands of discoveries made by mathematicians over the centuries, some stand out as significant landmarks. One of these is the prime number theorem, which describes the asymptotic distribution of prime numbers. It can be stated in various equivalent forms, two of which are: x (I) K(X) '" -I - as x --+ 00, ogx and Pn '" n log n as n --+ 00. (2) In (1), K(X) denotes the number of primes P ::s x for any x > O.

Keywords

algebra arithmetic boundary element method cryptography diophantine equation finite field form graphs homomorphism number theory polynomial prime number quadratic form story theorem

Editors and affiliations

  • R. P. Bambah
    • 1
  • V. C. Dumir
    • 1
  • R. J. Hans-Gill
    • 1
  1. 1.Centre for Advanced Study in MathematicsPanjab UniversityChandigarhIndia

Bibliographic information