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)


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.


Principal Part Dirichlet Series Simple Zero Riemann Hypothesis Analytic Number Theory 
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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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