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The least unramified prime which does not split completely

  • Asif Zaman ORCID logo EMAIL logo
Veröffentlicht/Copyright: 30. August 2017
Forum Mathematicum
Aus der Zeitschrift Forum Mathematicum Band 30 Heft 3

Abstract

Let K/F be a finite extension of number fields of degree n≥2. We establish effective field-uniform unconditional upper bounds for the least norm of a prime ideal 𝔭 of F which is degree 1 over ℚ and does not ramify or split completely in K. We improve upon the previous best known general estimates due to Li [7] when F=ℚ, and Murty and Patankar [9] when K/F is Galois. Our bounds are the first when K/F is not assumed to be Galois and F≠ℚ.

Keywords: Non-split prime; prime ideals
MSC 2010: 11R44; 11R42

Communicated by Jan Bruinier

Acknowledgements

The author would like to thank John Friedlander, Kumar Murty, and Jesse Thorner for their encouragement and helpful comments.

References

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Received: 2017-4-12
Revised: 2017-8-9
Published Online: 2017-8-30
Published in Print: 2018-5-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. A generalized uniqueness theorem and the graded ideal structure of Steinberg algebras
  3. Positive solutions for nonlinear nonhomogeneous parametric Robin problems
  4. Period relations for cusp forms of GSp4
  5. A generalization of a graph theory Mertens’ theorem: Galois covering case
  6. Commutators of the fractional integrals for second-order elliptic operators on Morrey spaces
  7. Vojta’s conjecture on rational surfaces and the abc conjecture
  8. The least unramified prime which does not split completely
  9. The ω-inequality problem for concatenation hierarchies of star-free languages
  10. Higher weight on GL(3). I: The Eisenstein series
  11. Fourier transforms of powers of well-behaved 2D real analytic functions
  12. Parabolic conformally symplectic structures I; definition and distinguished connections
  13. The quasi-arithmetic means and Cartan barycenters of compactly supported measures
  14. Estimates of lattice points in the discriminant aspect over abelian extension fields
  15. On Hecke eigenvalues of Siegel modular forms in the Maass space
  16. Harmonicity and minimality of complex and quaternionic radial foliations
https://doi.org/10.1515/forum-2017-0081
Schlagwörter für diesen Artikel
Non-split prime; prime ideals

Artikel in diesem Heft

  1. Frontmatter
  2. A generalized uniqueness theorem and the graded ideal structure of Steinberg algebras
  3. Positive solutions for nonlinear nonhomogeneous parametric Robin problems
  4. Period relations for cusp forms of GSp4
  5. A generalization of a graph theory Mertens’ theorem: Galois covering case
  6. Commutators of the fractional integrals for second-order elliptic operators on Morrey spaces
  7. Vojta’s conjecture on rational surfaces and the abc conjecture
  8. The least unramified prime which does not split completely
  9. The ω-inequality problem for concatenation hierarchies of star-free languages
  10. Higher weight on GL(3). I: The Eisenstein series
  11. Fourier transforms of powers of well-behaved 2D real analytic functions
  12. Parabolic conformally symplectic structures I; definition and distinguished connections
  13. The quasi-arithmetic means and Cartan barycenters of compactly supported measures
  14. Estimates of lattice points in the discriminant aspect over abelian extension fields
  15. On Hecke eigenvalues of Siegel modular forms in the Maass space
  16. Harmonicity and minimality of complex and quaternionic radial foliations
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