Sur les zéros des fonctions symétriques complètes (cas cubique)

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1. [1] I.O. Angell, A table of complex cubic fields, Bull. London Math. Soc.5 (1973), 37-38. Zbl0261.12007MR318099
2. [2] T. Azuhata, On the calculation of the units of algebraic number fields, Nagoya Math. J.101 (1986), 181-185. Zbl0576.12007MR828921
3. [3] E.T. Bell, Notes on recurring series of the third order, Tôhoku Math. J.24 (1924), 168-184. JFM50.0088.02
4. [4] J. Berstel et M. Mignotte, Deux propriétés décidables des suites récurrentes Linéaires, Bull. Soc. Math. France104 (1976), 175-184. Zbl0329.10009MR414475
5. [5] F. Beukers, The multiplicity of binary recurrences, Comp. Math.40 (1980), 251-267. Zbl0396.10005MR563543
6. [6] F. Beukers and R. Tijdeman, On the multiplicities of binary complex recurrences, Comp. Math.51 (1984), 193-213. Zbl0538.10014MR739734
7. [7] J.P. Bezivin, Sur un théorème de Pólya, J. Reine Angew. Math.364 (1986), 60-68. Zbl0569.10004MR817638
8. [8] E. Bombieri and W.M. Schmidt, On Thue's equation, Invent. Math.88 (1) (1987), 69-82. Zbl0614.10018MR877007
9. [9] Z.I. Borevitch et I.R. Chafarevitch, Théorie des Nombres, Gauthier-Villars, Paris, 1967. Zbl0145.04901MR205908
10. [10] R.D. Carmichael, On sequences of integers defined by recurrence relations, Quaterly J. Math.48 (1920), 343-372. 
11. [11] -----, On the numerical factors of the arithmetic forms αn ± βn, Annals of Math. series 2, 15 (1913), 30-70. JFM44.0216.01
12. [12] J.W.S. Cassels, Local fields, London Math. Soc. Stud. Texts 3, Cambridge Univ. Press, 1986. Zbl0595.12006MR861410
13. [13] L. Cerlienco, M. Mignotte et F. Piras, Suites récurrentes linéaires. Propriétés algébriques et arithmétiques, L'Enseignement Mathématique33 (1987), 67-108. Zbl0626.10008MR896384
14. [14] B.N. Delone and D.K. Fadeev, The theory of irrationalities of the third degree, Transl. Math. Mono., vol.10, A.M.S., 1964. Zbl0133.30202MR160744
15. [15] B. Deshommes, Sur les zéros des fonctions symétriques complètes (cas cubique) (1987), preprint. 
16. [16] M. Duboué, Une suite récurrente remarquable, Sémin. Delange-Pisot-Poitou1977/78, Paris, Exp. 27, 12pp. Zbl0396.10004MR520319
17. [17] J.H. Evertse, K. Györy, C.L. Stewart and R. Tijdeman, On S-unit equations in two unknowns (1987), preprint. Zbl0662.10012MR939471
18. [18] B. Gordon and S.P. Mohanty, On a theorem of Delaunay and some related results, Pacific J. Math.68 (2) (1977), 399-409. Zbl0369.12003MR463109
19. [19] O. Hemer, Notes on the Diophantine equation y2-k = x3, Arkiv för Mat.3 (3) (1954), 67-77. Zbl0055.03607MR61115
20. [20] K.K. Kubota, On a conjecture of Morgan Ward I, II, III, Acta Arith.33 (1977), 11-28, 29-48, 99-109. Zbl0356.10007MR441842
21. [21] A. Lascoux, Suites récurrentes linéaires, Advances in Applied Math. (1986), 1-8. Zbl0605.10005MR845379
22. [22] M. Laurent, Equations exponentielles polynômes et suites récurrentes linéaires, Soc. Math. de France, Astérisque147-148 (1987), 121-139. Zbl0621.10014MR891424
23. [23] D.J. Lewis and J. Turk, Repetitiveness in binary recurrences, J. Reine Angew. Math.356 (1985), 19-48. Zbl0551.10012MR779374
24. [24] I.G. Macdonald, Symmetric functions and Hall polynomials, Oxford Math. Mono., 1979. Zbl0487.20007MR553598
25. [25] K. Mahler, On the Taylor coefficients of rational functions, Proc. Cambridge Phil. Soc.52 (1956), 39-48. Zbl0070.04004MR74503
26. [28] M. Mignotte, Suites récurrentes linéaires, Sémin. Delange-Pisot-Poitou1973/74, Paris, Exp. G 14, 9pp. Zbl0318.10005
27. [27] -----, Détermination des répétitions d'une certaine suite récurrente linéaire, Publicationes Mathematicae33 (Debrecen, 1986), 297-306. Zbl0626.10009MR883759
28. [28] M. Mignotte, T.N. Shorey and R. Tijdeman, The distance between terms of an algebraic recurrence sequence, J. Reine Angew Math.349 (1984), 63-76. Zbl0521.10011MR743965
29. [29] L.J. Mordell, Diophantine equations, Academic Press, London, 1969. Zbl0188.34503MR249355
30. [30] T. Magell, L'analyse indéterminée de degré supérieur, Mémorial Sc. Math., vol.39, Gauthier-Villars, Paris, 1929. JFM55.0712.02
31. [31] P.A. Picon, Sur les termes nuls d'une suite récurrente cubique, Rairo R-3, (1974), 47-61. Zbl0316.65033MR369244
32. [32] -----, Sur certaines suites récurrentes cubiques ayant deux ou trois termes nuls, Discrete Math.21 (1978), 285-296. Zbl0382.10010MR522902
33. [33] A.J. Van der Poorten, Some problems of recurrent interest, Topics in classical number theory, vol. I, II (Budapest, 1981), 1265-1294, Coll. Math. Soc. János Bolyai, 34, North. Holland, Amsterdam-New York, 1984. Zbl0543.10007MR781185
34. [34] P. Robba, Nombre de zéros des fonctions exponentielles-polynômes, Groupe d'étude d'Analyse ultramétrique, 4eannée, 1976/77, n 9, 3p. Zbl0381.12010
35. [35] -----, Zéros des suites récurrentes linéaires, Groupe d'étude d'Analyse ultramétrique, 5eannée, 1977/78, n° 13, 5p. Zbl0402.10007
36. [36] M. Scarowsky, On units of certain cubic fields and the diophantine equation x3+y3+z3 = 3, Proc. Amer. Math. Soc.91 (1984), 351-356. Zbl0541.10020MR744627
37. [37] S.J. Scott , On the number of zeros of a cubic recurrence, Amer. Math. Monthly67 (1960), 169-170. Zbl0098.26201MR118696
38. [38] D. Shanks, A survey of quadratic, cubic and quartic algebraic number fields, Proc. 7th S-E Conf. Combinatorics, Graph Theory, and Computing, Louisiana State Univ. Baton Rouge, (february 1976), 15-40. Zbl0357.12004MR453691
39. [39] T.N. Shorey and R. Tijdeman, Exponential diophantine equations, Cambridge Tracts in Math.87, Cambridge Univ. Press, 1986. Zbl0606.10011MR891406
40. [40] J.H. Silverman, Integer points and the rank of Thue elliptic curves, Invent. Math.66 (1982), 395-404. Zbl0494.14008MR662599
41. [41] R. Smadja, Calculs effectifs sur les idéaux des corps de nombres algébriques, Marseille-Luminy (mars 1976). Zbl0348.12019
42. [42] M.F. Smiley, On the zeros of a cubic recurrence, Amer. Math. Monthly63 (1956), 171-172. Zbl0070.27302MR75967
43. [43] R. Tijdeman, Multiplicities of binary recurrences, Sémin. Théor. Nombres, Univ. Bordeaux I, 1980/1981, Exp. 29, 11pp. Zbl0473.10012MR644662
44. [44] N.K. Vereshchagin, Occurrence of zero in a linear recursive sequence, Mat. Zametki vol. 38 (2) (1985), 177-189. Zbl0595.10007MR808885
45. [45] -----, Effective upper bounds for the number of zeros of a linear recursive sequence, Vestnik Moskov. Univ. Mat. vol.41 (1) (1986), 33-38. Zbl0605.10006
46. [46] M. Ward, Notes on an arithmetical property of recurring series, Math. Zeitschrift39 (1934), 212-214. Zbl0010.00802JFM60.0919.04
47. [47] -----, On the number of vanishing terms in an integral cubic recurrence, Amer. Math. Monthly62 (1955), 155-160. Zbl0064.04008MR67136
48. [48] -----, The vanishing of the homogeneous product sum of the roots of a cubic, Duke Math. J.26 (1959), 553-562. Zbl0093.04701MR110669
49. [49] -----, The vanishing of the homogeneous product sum on three letters, Duke Math. J.27 (1960), 619-624. Zbl0097.03004MR114790
50. [50] -----, Some Diophantine problems connected with linear recurrences, Report Institute Th. Numbers, Univ. Colorado, Boulder (1959), 250-257.