An effective lower bound for the height of algebraic numbers

Paul Voutier

Acta Arithmetica (1996)

  • Volume: 74, Issue: 1, page 81-95
  • ISSN: 0065-1036

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Paul Voutier. "An effective lower bound for the height of algebraic numbers." Acta Arithmetica 74.1 (1996): 81-95. <http://eudml.org/doc/206839>.

@article{PaulVoutier1996,
author = {Paul Voutier},
journal = {Acta Arithmetica},
keywords = {algebraic number; absolute logarithmic height; Mahler measure},
language = {eng},
number = {1},
pages = {81-95},
title = {An effective lower bound for the height of algebraic numbers},
url = {http://eudml.org/doc/206839},
volume = {74},
year = {1996},
}

TY - JOUR
AU - Paul Voutier
TI - An effective lower bound for the height of algebraic numbers
JO - Acta Arithmetica
PY - 1996
VL - 74
IS - 1
SP - 81
EP - 95
LA - eng
KW - algebraic number; absolute logarithmic height; Mahler measure
UR - http://eudml.org/doc/206839
ER -

References

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  1. [1] M. J. Bertin et M. Pathiaux-Delefosse, Conjecture de Lehmer et petits nombres de Salem, Queen's Papers in Pure and Appl. Math. 81, Kingston, 1989. Zbl0707.11073
  2. [2] P. E. Blanksby and H. L. Montgomery, Algebraic integers near the unit circle, Acta Arith. 18 (1971), 355-369. Zbl0221.12003
  3. [3] D. W. Boyd, Reciprocal polynomials having small measure, Math. Comp. 35 (1980), 1361-1377. Zbl0447.12002
  4. [4] D. W. Boyd, Reciprocal polynomials having small measure. II, Math. Comp. 53 (1989), 355-357. Zbl0684.12003
  5. [5] D. C. Cantor and E. G. Straus, On a conjecture of D. H. Lehmer, Acta Arith. 42 (1982), 97-100; corrigendum, Math. Comp., 327. 
  6. [6] E. Dobrowolski, On a question of Lehmer and the number of irreducible factors of a polynomial, Math. Comp. 34 (1979), 391-401. Zbl0416.12001
  7. [7] A. Dubickas, On a conjecture of A. Schinzel and H. Zassenhaus, Math. Comp. 63 (1993), 15-20. 
  8. [8] M. Laurent, M. Mignotte et Y. Nesterenko, Formes linéaires en deux logarithmes et déterminant d'interpolation, J. Number Theory, to appear. 
  9. [9] D. H. Lehmer, Factorization of certain cyclotomic functions, Ann. of Math. (2) 34 (1933), 461-479. Zbl0007.19904
  10. [10] R. Louboutin, Sur la mesure de Mahler d'un nombre algébrique, C. R. Acad. Sci. Paris Sér. I 296 (1983), 707-708. Zbl0557.12001
  11. [11] E. M. Matveev, On the measure of algebraic integers, Mat. Zametki 49 (1991), 152-154 (in Russian). Zbl0732.11052
  12. [12] M. Meyer, Le problème de Lehmer: méthode de Dobrowolski et lemme de Siegel 'à la Bombieri-Vaaler', Publ. Math. Univ. P. et M. Curie (Paris VI), 90, Problèmes Diophantiens 1988/89, N°5, 15 p. 
  13. [13] G. Poitou, Minorations de discriminants [d'après A.M. Odlyzko ], Séminaire Bourbaki 479, Lecture Notes in Math. 567, Springer, 1977, 136-153. 
  14. [14] G. Robin, Estimation de la fonction de Tchebychef θ sur le k-ième nombre premier et grandes valeurs de la fonction ω(n) nombre de diviseurs premiers de n, Acta Arith. 42 (1983), 367-389. 
  15. [15] J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94. Zbl0122.05001
  16. [16] A. Schinzel and H. Zassenhaus, A refinement of two theorems of Kronecker, Michigan Math. J. 12 (1965), 81-85. Zbl0128.03402
  17. [17] C. J. Smyth, On the product of the conjugates outside the unit circle of an algebraic integer, Bull. London Math. Soc. 3 (1971), 169-175. Zbl0235.12003
  18. [18] C. L. Stewart, Algebraic integers whose conjugates lie near the unit circle, Bull. Soc. Math. France 106 (1978), 169-176 Zbl0396.12002

Citations in EuDML Documents

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  1. Florian Luca, Diego Marques, Perfect powers in the summatory function of the power tower
  2. Gaël Rémond, Christine Zehrt-Liebendörfer, Le théorème de Schanuel pour un corps non commutatif
  3. Yann Bugeaud, Kálmán Győry, Bounds for the solutions of Thue-Mahler equations and norm form equations
  4. Nicolas Ratazzi, Problème de Lehmer sur 𝔾 m et méthode des pentes
  5. Artūras Dubickas, The mean values of logarithms of algebraic integers
  6. Francesco Amoroso, Sinnou David, Minoration de la hauteur normalisée des hypersurfaces
  7. Yann Bugeaud, Florian Luca, Maurice Mignotte, Samir Siksek, Almost powers in the Lucas sequence

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