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Handbook of Number Theory I

  • Reference work
  • © 2006

Overview

Authors:
  1. József Sándor

    1. Babes-Bolyai University of Cluj, Cluj-Napoca, Romania

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  2. Dragoslav S. Mitrinović

    1. University of Belgrade, Servia, Yugoslavia

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  3. Borislav Crstici

    1. Technical University of Timisoara, Timisoara, Romania

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About this book

This handbook covers a wealth of topics from number theory, special attention being given to estimates and inequalities. As a rule, the most important results are presented, together with their refinements, extensions or generalisations. These may be applied to other aspects of number theory, or to a wide range of mathematical disciplines. Cross-references provide new insight into fundamental research.

Audience: This is an indispensable reference work for specialists in number theory and other mathematicians who need access to some of these results in their own fields of research.

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Table of contents (16 entries)

  1. Front Matter

    Pages i-7
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  2. Euler’s ϕ-Function

    Pages 9-37

  3. The Arithmetical Function d(N), Its Generalizations and Its Analogues

    Pages 39-75

  4. Sum-of-Divisors Function, Generalizations, Analogues; Perfect Numbers and Related Problems

    Pages 77-120

  5. P, p, B, β and Related Functions

    Pages 121-154

  6. ω (n), Ω (n) and Related Functions

    Pages 155-185

  7. Function μ; k-Free And k-Full Numbers

    Pages 187-226

  8. Functions π(x), ψ(x), θ(x), and the Sequence of Prime Numbers

    Pages 227-274

  9. Primes in Arithmetic Progressions and other Sequences

    Pages 275-311

  10. Additive and Diophantine Problems Involving Primes

    Pages 313-348

  11. Exponential Sums

    Pages 349-388

  12. Character Sums

    Pages 389-416

  13. Binomial Coefficients, Consecutive Integers and Related Problems

    Pages 417-457

  14. Estimates Involving Finite Groups and Semi-Simple Rings

    Pages 459-490

  15. Partitions

    Pages 491-521

  16. Congruences, Residues and Primitive Roots

    Pages 523-556

  17. Additive and Multiplicative Functions

    Pages 557-610

  18. Back Matter

    Pages 611-622
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Authors and Affiliations

  • Babes-Bolyai University of Cluj, Cluj-Napoca, Romania

    József Sándor

  • University of Belgrade, Servia, Yugoslavia

    Dragoslav S. Mitrinović

  • Technical University of Timisoara, Timisoara, Romania

    Borislav Crstici

Bibliographic Information

  • Book Title: Handbook of Number Theory I

  • Authors: József Sándor, Dragoslav S. Mitrinović, Borislav Crstici

  • DOI: https://doi.org/10.1007/1-4020-3658-2

  • Publisher: Springer Dordrecht

  • eBook Packages: Mathematics and Statistics, Reference Module Computer Science and Engineering

  • Copyright Information: Springer Science+Business Media B.V. 2006

  • Hardcover ISBN: 978-1-4020-4215-7Published: 17 November 2005

  • eBook ISBN: 978-1-4020-3658-3Published: 21 September 2006

  • Edition Number: 1

  • Number of Pages: XXVI, 622

  • Additional Information: Originally pulished as volume 351 in the series "Mathematics and Its Applications"

  • Topics: Number Theory, Algebra

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