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Birkhäuser

Number Theory

  • Book
  • © 2000

Overview

Editors:
  1. R. P. Bambah

    1. Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India

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  2. V. C. Dumir

    1. Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India

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    You can also search for this editor in PubMed   Google Scholar

  3. R. J. Hans-Gill

    1. Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India

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Part of the book series: Trends in Mathematics (TM)

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Table of contents (23 chapters)

  1. Front Matter

    Pages i-vii
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  2. A Centennial History of the Prime Number Theorem

    • Tom M. Apostol
    Pages 1-14

  3. Non-homogeneous Problems: Conjectures of Minkowski and Watson

    • R. P. Bambah, V. C. Dumir, R. J. Hans-Gill
    Pages 15-41

  4. On the Oscillation Theorems of Pringsheim and Landau

    • Paul T. Bateman, Harold G. Diamond
    Pages 43-54

  5. Modular Equations in Ramanujan’s Lost Notebook

    • Bruce C. Berndt
    Pages 55-74

  6. The abc-conjecture

    • Jerzy Browkin
    Pages 75-105

  7. On Values of Linear and Quadratic Forms at Integral Points

    • S. G. Dani
    Pages 107-119

  8. Variants of the Second Borel-Cantelli Lemma and their Applications in Metric Number Theory

    • Glyn Harman
    Pages 121-140

  9. Pythagorean Triples

    • Edmund Hlawka
    Pages 141-155

  10. Integer Points in Plane Regions and Exponential Sums

    • M. N. Huxley
    Pages 157-166

  11. Artin’s Conjecture for Polynomials Over Finite Fields

    • Erik Jensen, M. Ram Murty
    Pages 167-181

  12. Continuous Homomorphisms as Arithmetical Functions, and Sets of Uniqueness

    • I. Kátai
    Pages 183-200

  13. Hamburger’s Theorem on ζ(s) and the Abundance Principle for Dirichlet Series with Functional Equations

    • Marvin I. Knopp
    Pages 201-216

  14. A Survey of Number Theory and Cryptography

    • Neal Koblitz
    Pages 217-239

  15. Recent Developments in the Mean Square Theory of the Riemann Zeta and Other Zeta-Functions

    • Kohji Matsumoto
    Pages 241-286

  16. Algebraic Curves Over Finite Fields with many Rational Points and their Applications

    • Harald Niederreiter, Chaoping Xing
    Pages 287-300

  17. A Report on Artin’s Holomorphy Conjecture

    • Dipendra Prasad, C. S. Yogananda
    Pages 301-314

  18. Siegel’s Main Theorem for Quadratic Forms

    • S. Raghavan
    Pages 315-324

  19. Pfister’s Work on Sums of Squares

    • A. R. Rajwade
    Pages 325-349

  20. Notes on the Prime Number Theorem-I

    • K. Ramachandra
    Pages 351-370
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Keywords

About this book

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.

Editors and Affiliations

  • Centre for Advanced Study in Mathematics, Panjab University, Chandigarh, India

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

Bibliographic Information

  • Book Title: Number Theory

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

  • Series Title: Trends in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-7023-8

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 2000

  • Softcover ISBN: 978-3-0348-7025-2Published: 22 July 2012

  • eBook ISBN: 978-3-0348-7023-8Published: 06 December 2012

  • Series ISSN: 2297-0215

  • Series E-ISSN: 2297-024X

  • Edition Number: 1

  • Number of Pages: VII, 527

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Algebra

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