Chebyshev's method for number fields

José Felipe Voloch

Journal de théorie des nombres de Bordeaux (2000)

  • Volume: 12, Issue: 1, page 81-85
  • ISSN: 1246-7405

Abstract

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We give an elementary proof of an explicit estimate for the number of primes splitting completely in an extension of the rationals. The proof uses binomial coefficents and extends Chebyshev's classical approach.

How to cite

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Voloch, José Felipe. "Chebyshev's method for number fields." Journal de théorie des nombres de Bordeaux 12.1 (2000): 81-85. <http://eudml.org/doc/248512>.

@article{Voloch2000,
abstract = {We give an elementary proof of an explicit estimate for the number of primes splitting completely in an extension of the rationals. The proof uses binomial coefficents and extends Chebyshev's classical approach.},
author = {Voloch, José Felipe},
journal = {Journal de théorie des nombres de Bordeaux},
language = {eng},
number = {1},
pages = {81-85},
publisher = {Université Bordeaux I},
title = {Chebyshev's method for number fields},
url = {http://eudml.org/doc/248512},
volume = {12},
year = {2000},
}

TY - JOUR
AU - Voloch, José Felipe
TI - Chebyshev's method for number fields
JO - Journal de théorie des nombres de Bordeaux
PY - 2000
PB - Université Bordeaux I
VL - 12
IS - 1
SP - 81
EP - 85
AB - We give an elementary proof of an explicit estimate for the number of primes splitting completely in an extension of the rationals. The proof uses binomial coefficents and extends Chebyshev's classical approach.
LA - eng
UR - http://eudml.org/doc/248512
ER -

References

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  1. [C] P.L. Chebyshev, Memoire sur les nombres premiers. J. Math. pures et appl.17 (1852), 366-390. 
  2. [CC] D. Chudnovsky, G. Chudnovsky, Applications of Padé approximations to the Grothendieck conjecture on linear differential equations. In Number theory (New York, 1983-84), 52-100, Lecture Notes in Math.1135, Springer, Berlin-New York, 1985. Zbl0565.14010MR803350
  3. [DFI] W. Duke, J.B. Friedlander, H. Iwaniec, Equidistribution of roots of a quadratic congruence to prime moduli, Ann. of Math.141 (1995), 423-441. Zbl0840.11003MR1324141
  4. [F] J.B. Friedlander, Estimates for Prime Ideals. J. Number Theory, 12 (1980), 101-105. Zbl0428.12010MR566874
  5. [L] E. Landau, Über die zu einem algebraischen Zahlkörper gehörige Zetafunktion und die Ausdehnung der Tschebyscheffschen Primzahlentheorie auf das Problem der Verteilung der Primideale. Crelle125 (1903), 64-188. JFM33.0215.01
  6. [P] H. Poincaré, Extension aux nombres premiers complexes des Théorèmes de M. Tchebicheff. J. Math. Pures Appl. (4) 8 (1892), 25-68. JFM24.0171.02
  7. [VV] J. Vaaler, J.F. Voloch, The least nonsplit prime in Galois extensions of Q. J. Number Theory, to appear. Zbl0963.11066MR1802720

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