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The (α, β)-ramification invariants of a number field

  • Guillermo Mantilla-Soler EMAIL logo
Published/Copyright: January 29, 2021
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 71 Issue 1

Abstract

Let L be a number field. For a given prime p, we define integers αpL and βpL with some interesting arithmetic properties. For instance, βpL is equal to 1 whenever p does not ramify in L and αpL is divisible by p whenever p is wildly ramified in L. The aforementioned properties, although interesting, follow easily from definitions; however a more interesting application of these invariants is the fact that they completely characterize the Dedekind zeta function of L. Moreover, if the residue class mod p of αpL is not zero for all p then such residues determine the genus of the integral trace.

Keywords: Arithmetic invariants of number fields; Dedekind zeta functions
MSC 2010: Primary 11R04; 11R42; 11R56

  1. (Communicated by Milan Paštéka)

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Received: 2019-11-04
Accepted: 2020-05-14
Published Online: 2021-01-29
Published in Print: 2021-02-23

© 2021 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2017-0464
Keywords for this article
Arithmetic invariants of number fields; Dedekind zeta functions

Articles in the same Issue

  1. Regular papers
  2. Prof. RNDr. Ing. Lubomír Kubáček, DrSc., Dr.h.c. –Nonagenarian
  3. Doc. RNDr. Roman Frič, DrSc. passed away
  4. Outer and inner approximations in quantum spaces
  5. Linear derivations on Banach *-algebras
  6. New fractional order discrete Grüss type inequality
  7. Exponential trigonometric convex functions and Hermite-Hadamard type inequalities
  8. Generalized Minkowski type inequality for pseudo-integral
  9. Study of the Q-spiral-like functions of complex order
  10. Radius of starlikeness of certain analytic functions
  11. Successive approximations for a differential equation in a Banach space via Constantin condition
  12. Approximation of the multi-m-Jensen-quadratic mappings and a fixed point approach
  13. Oscillation and asymptotic behavior of a higher-order neutral delay difference equation with variable delays under Δm
  14. Sequence selection properties in Cp(X) with the double ideals
  15. On the paranormed Nörlund difference sequence space of fractional order and geometric properties
  16. On certain Diophantine equations concerning the area of right triangles
  17. Weighted projective Ricci curvature in Finsler geometry
  18. Euler classes of vector bundles over manifolds
  19. A new generalized Lindley-Weibull class of distributions: Theory, properties and applications
  20. Dynamical behaviors of a prey-predator model with foraging arena scheme in polluted environments
  21. The (α, β)-ramification invariants of a number field
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