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p-adic L-functions and Bernoulli Numbers

  • Lawrence C. Washington
Part of the Graduate Texts in Mathematics book series (GTM, volume 83)

Abstract

In this chapter we shall construct p-adic analogues of Dirichlet L-functions. Since the usual series for these functions do not converge p-adically, we must resort to another procedure. The values of \( L\left( {s,\chi } \right)\) at negative integers are algebraic, hence may be regarded as lying in an extension of \( {\mathbb{Q}_p}\). We therefore look for a p-adic function which agrees with \( L\left( {s,\chi } \right)\) at the negative integers. With a few minor modifications, this is possible.

Keywords

Class Number Bernoulli Number Dirichlet Character Rational Integer Class Field Theory 
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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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Lawrence C. Washington
    • 1
  1. 1.Mathematics DepartmentUniversity of MarylandCollege ParkUSA

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