Elementary Properties of the Zeta Function and L-series

  • Serge Lang
Part of the Graduate Texts in Mathematics book series (GTM, volume 110)


We recall the formula for summation by parts. If {a n } and {b n } are sequences of complex numbers, and if we let
be the partial sums, then
We shall consider series
where {a n } is a sequence of complex numbers, and s is a complex variable. We write s = σ + it with σ, t real.


Zeta Function Number Field Dirichlet Series Arithmetic Progression Class Field 
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Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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