In this introduction we give some hints for the importance of the Riemann zeta-function for analytic number theory and present first classic results on its amazing value-distribution due to Harald Bohr but also the remarkable universality theorem of Voronin (including a sketch of his proof). Moreover, we introduce Dirichlet L-functions and other generalizations of the zeta-function, discuss their relevance in number theory and comment on their value-distribution. For historical details we refer to Narkiewicz's monograph [277] and Schwarz's surveys [317, 318].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
(2007). Introduction. In: Value-Distribution of L-Functions. Lecture Notes in Mathematics, vol 1877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44822-8_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-44822-8_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26526-9
Online ISBN: 978-3-540-44822-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)