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Mathematische Zeitschrift

, Volume 292, Issue 1–2, pp 183–192 | Cite as

A note on the least prime that splits completely in a nonabelian Galois number field

  • Zhenchao Ge
  • Micah B. MilinovichEmail author
  • Paul Pollack
Article
  • 56 Downloads

Abstract

We prove a nontrivial estimate for the size of the least rational prime that splits completely in the ring of integers of certain families of nonabelian Galois number fields. Our result complements results of Linnik and Vinogradov and of Pollack who studied this problem in the quadratic and abelian number field settings, respectively.

Keywords

Primes Split completely Number fields Dedekind zeta-function Subconvexity 

Mathematics Subject Classification

11R42 11R44 11F66 11M20 

Notes

Acknowledgements

This project began as a result of an SEC Faculty Travel Grant that allowed the second author to visit the University of Georgia. We thank the Southeastern Conference for its support. We also thank Caroline Turnage-Butterbaugh, Jesse Thorner, and the anonymous referee for a number of useful comments.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Zhenchao Ge
    • 1
  • Micah B. Milinovich
    • 1
    Email author
  • Paul Pollack
    • 2
  1. 1.Department of MathematicsUniversity of MississippiUniversityUSA
  2. 2.Department of MathematicsUniversity of GeorgiaAthensUSA

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