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Introduction

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1877)

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].

Keywords

  • Modular Form
  • Cusp Form
  • Dirichlet Series
  • Critical Line
  • Riemann Hypothesis

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© 2007 Springer-Verlag Berlin Heidelberg

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(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

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