Number Theoretic Background

  • Andreas Knauf
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 618)


This paper is an expanded version of some of the lectures given at the summer school in Bologna. In these lectures we gave an introduction to very basic number theory, assuming practically no background. The lectures were intended for graduate students in Math and Physics and while the material is completely standard, we tried to make the presentation as elementary as possible.

Some of the easier proofs are included, others are relegated to exercises, but several of the deeper facts are stated without proof. Most of the material may be found in classic texts such as [1] and [3].


Fundamental Solution Integer Solution Great Common Divisor Primitive Root Riemann Hypothesis 
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  1. 1.
    H. Davenport, The higher arithmetic, Seventh edition, Cambridge Univ. Press, Cambridge, 1999.zbMATHGoogle Scholar
  2. 2.
    H. M. Edwards Riemann’s Zeta Function, Academic Press 1974.Google Scholar
  3. 3.
    G.H. Hardy and E.M. Wright, An introduction to the theory of numbers (The Clarendon Press, Oxford University Press, New York, 1979).zbMATHGoogle Scholar
  4. 4.
    M. Murty Artin’s conjecture for primitive roots Math. Intelligencer 10 (1988), no. 4, 59–67.zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    B. Riemann Über die Anzahl der Primzahlen unter einer gegebenen Größe, Montasb. der Berliner Akad. (1858/60) 671–680, in Gessamelte Mathematische Werke 2nd edition, Teubner, Leipzig 1982 no. VII.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Andreas Knauf
    • 1
  1. 1.Mathematisches InstitutUniversität Erlangen-NürnbergErlangenGermany

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