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Introduction

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1471)

Abstract

The starting point in the theory of zeta functions is the expansion of the Rieman zeta-function ζ(s) into the Euler product:

$$\varsigma (s) = \mathop \prod \limits_p (1 - p^{ - s} )^{ - 1} = \sum\limits_{n = 1}^\infty {n^{ - s} } (\operatorname{Re} (s) > 1)$$

The set of arguments s for which ζ(s) is defined can be extended to all s ∈ C,s ≠ 1, and we may regard C as the group of all continuous quasicharacters

$$C = Hom(R_ + ^ \times ,C^ \times ),y \mapsto y^8 $$

of R ×+ .

Keywords

  • Zeta Function
  • Galois Group
  • Eisenstein Series
  • Cusp Form
  • Automorphic Form

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1991 Springer-Verlag Berlin Heidelberg

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Panchishkin, A.A. (1991). Introduction. In: Non-Archimedean L-Functions of Siegel and Hilbert Modular Forms. Lecture Notes in Mathematics, vol 1471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21541-8_1

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  • DOI: https://doi.org/10.1007/978-3-662-21541-8_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54137-0

  • Online ISBN: 978-3-662-21541-8

  • eBook Packages: Springer Book Archive