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Simple Zeros of the Zeta-Function of a Quadratic Number Field, II

  • J. B. Conrey
  • A. Ghosh
  • S. M. Gonek
Part of the Progress in Mathematics book series (PM, volume 70)

Abstract

Let K be a fixed quadratic extension of Q and write ζK(s) for the Dedekind zeta-function of K, where s = σ + it. It is wellknown, and easy to prove, that the number NK(T) of zeros of ζK(s) in the region 0 < σ < 1, 0 < t ≤ T satisfies
$${{\text{N}}_{\text{K}}}\left( {\text{T}} \right)\frac{{\text{T}}}{\pi } \log T$$
as T → ∞. On the other hand, not much is known about the number of \(\text{N}_\text{K}^\text{*} \left( \text{T} \right)\) that are simple.

Keywords

Principal Part Dirichlet Series Simple Zero Riemann Hypothesis Analytic Number 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

© Birkhäuser Boston 1987

Authors and Affiliations

  • J. B. Conrey
    • 1
  • A. Ghosh
    • 1
  • S. M. Gonek
    • 2
  1. 1.Okalhoma State UniversityStillwaterUSA
  2. 2.University of RochesterRochesterUSA

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