p-adic L-functions and Bernoulli Numbers

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


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.


Class Number Bernoulli Number Dirichlet Character Rational Integer Class Field Theory 
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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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