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Berstel, Jean; Mignotte, Maurice

Deux propriétés décidables des suites récurrentes linéaires. (French) Zbl 0329.10009

Bull. Soc. Math. Fr. 104, 175-184 (1976).
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scan of Zbl 0329.10009

Cited in 2 Reviews
Cited in 33 Documents

MSC:

11B37 Recurrences
11U05 Decidability (number-theoretic aspects)
03B25 Decidability of theories and sets of sentences
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\textit{J. Berstel} and \textit{M. Mignotte}, Bull. Soc. Math. Fr. 104, 175--184 (1976; Zbl 0329.10009)
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References:

[1] BENZAGHOU (B.) . - Algèbres de Hadamard , Bull. Soc. math. France, t. 98, 1970 , p. 209-252. Numdam | MR 44 #1658 | Zbl 0206.33203 · Zbl 0206.33203
[2] BERSTEL (J.) . - Factorisation de fractions rationnelles et de suites récurrentes , Acta Arithmetica, t. 30, 1976 , p. 5-17. Article | MR 54 #2572 | Zbl 0336.10009 · Zbl 0336.10009
[3] EILENBERG (S.) . - Automata, languages and machines . Vol. A : Foundations. - New York, Academic Press, 1973 (Pure and applied Mathematics Series, 59). MR 58 #26604b | Zbl 0317.94045 · Zbl 0317.94045
[4] LECH (C.) . - A note on recurring series , Arkiv der Math., t. 2, 1953 , p. 417-421. MR 15,104e | Zbl 0051.27801 · Zbl 0051.27801
[5] LEWIS (D. J.) . - Diophantine equations, p-adic methods , “Studies in Number Theory”, [W. J. LE VEQUE, ed.], p. 25-75. - New York, Prentice Hall, 1969 (MAA Studies in Mathematics, 6). MR 39 #2699 | Zbl 0218.10035 · Zbl 0218.10035
[6] MAHLER. (K.) . - Eine arithmetische Eigenschaft der Taylor-Koeffizienten rationaler Funktionen , Koninkl. Akad. Wetensch. Amsterdam, Proc., t. 38, 1935 , p. 50-60. Zbl 0010.39006 | JFM 61.0176.02 · Zbl 0010.39006
[7] MIGNOTTE (M.) . - A note on linear recursive series , J. Austr. math. Soc (à paraître). Zbl 0305.10009 · Zbl 0305.10009
[8] MIGNOTTE (M.) . - Suites récurrentes linéaires , Séminaire Delange-Pisot-Poitou: Groupe d’études de théorie des nombres, 15e année, 1973 / 1974 , n^\circ G 14, 9 p. Numdam | Zbl 0318.10005 · Zbl 0318.10005
[9] MIGNOTTE (M.) . - Algorithmes relatifs à la décomposition des polynômes , “Theoretical Computer Science” (à paraître). Zbl 0324.65020 · Zbl 0324.65020
[10] PICON (P. A.) . - Sur les termes nuls d’une suite récurrente cubique , R.A.I.R.O., 8e année, R-3, 1974 , p. 47-61. Numdam | MR 51 #5479 | Zbl 0316.65033 · Zbl 0316.65033
[11] PISOT (C.) . - Quelques aspects de la théorie des entiers algébriques . - Montréal, les Presses Universitaires de Montréal, 1963 (Séminaire de Mathématiques supérieures. été 1963 , 5). MR 39 #6854 | Zbl 0141.04701 · Zbl 0141.04701
[12] PÓLYA (G.) . - Arithmetische Eigenschaften der Reihenentwicklungen rationaler Funktionen , J. reine und ang. Math., t. 151, 1921 , p. 1-31. JFM 47.0276.02 · JFM 47.0276.02
[13] PÓLYA (G.) et SZEGÖ (G.) . - Aufgaben und Lehrsätze aus der Analysis , 3te Auflage. -. Berlin, Springer-Verlag, 1964 (Heidelberger Taschenbücher, 73, 74). · Zbl 0122.29704
[14] ROSSER (J. B.) and SCHOENFELD (L.) . - Approximate formulas for some functions of prime numbers , Illinois J. Math., t. 6, 1962 , p. 64-94. Article | MR 25 #1139 | Zbl 0122.05001 · Zbl 0122.05001
[15] SIEGEL (C. L.) . - Über die Koeffizienten in der Taylorentwicklung rationaler Funktionen , Tôhoku math. J., t. 20, 1921 , p. 26-31. JFM 48.0329.01 · JFM 48.0329.01
[16] SHAPIRO. (H. N.) - On a theorem concerning exponential polynomials , Comm. pure and appl. Math., t. 12, 1959 , p. 487-500. MR 22 #12078 | Zbl 0086.25904 · Zbl 0086.25904
[17] SKOLEM (T.) . - Ein Verfahren zur Behandlung gewisser exponentialer Gleichungen , ”Comptes Rendus du 8e Congrès des Mathématiciens scandinaves, Stockholm 1934 ”, p. 163-188. - Lund, Håkan Ohlssons, 1935 . Zbl 0011.39201 | JFM 61.1080.01 · Zbl 0011.39201
[18] SMILEY (M. F.) . - On the zeros of a cubic recurrence , Amer. math. Monthly, t. 63, 1956 , p. 171-172. MR 17,826e | Zbl 0070.27302 · Zbl 0070.27302
[19] WARD (M.) . - Note on an arithmetical property of recurring series , Math. Z., t. 39, 1934 , p. 211-224. Zbl 0010.00802 | JFM 60.0919.04 · Zbl 0010.00802
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