Abstract
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].
or -|b|/2 < r ≤ |b|/2.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
H. Davenport, The higher arithmetic, Seventh edition, Cambridge Univ. Press, Cambridge, 1999.
H. M. Edwards Riemann’s Zeta Function, Academic Press 1974.
G.H. Hardy and E.M. Wright, An introduction to the theory of numbers (The Clarendon Press, Oxford University Press, New York, 1979).
M. Murty Artin’s conjecture for primitive roots Math. Intelligencer 10 (1988), no. 4, 59–67.
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.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Knauf, A. (2003). Number Theoretic Background. In: Esposti, M.D., Graffi, S. (eds) The Mathematical Aspects of Quantum Maps. Lecture Notes in Physics, vol 618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-37045-5_2
Download citation
DOI: https://doi.org/10.1007/3-540-37045-5_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-02623-5
Online ISBN: 978-3-540-37045-1
eBook Packages: Springer Book Archive