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Volumn 218, Issue 1, 1999, Pages 143-160

Transcendence of formal power series with rational coefficients

(1)  Allouche, J P a  

a CNRS   (France)

Author keywords

Automatic sequences; Binomial series; Chomsky Sch tzenberger theorem; p Lucas sequences; Transcendental formal power series

Indexed keywords


EID: 0347022546     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(98)00256-4     Document Type: Article
Times cited : (21)

References (67)
  • 5
    • 0028764196 scopus 로고
    • Canonical positions for the factors in the paper-folding sequences
    • J.-P. Allouche, M. Bousquet-Mélou, Canonical positions for the factors in the paper-folding sequences, Theoret. Comput. Sci. 129 (1994) 263-278.
    • (1994) Theoret. Comput. Sci. , vol.129 , pp. 263-278
    • Allouche, J.-P.1    Bousquet-Mélou, M.2
  • 8
    • 85034564723 scopus 로고    scopus 로고
    • to appear
    • J.-P. Allouche, D. Gouyou-Beauchamps, G. Skordev, Transcendence of binomial and Lucas' formal power series, Rapport de Recherche du LRI 1153 (February 1998), Orsay, J. Algebra, to appear.
    • J. Algebra
    • Orsay1
  • 10
    • 1842629181 scopus 로고    scopus 로고
    • Automata and transcendence of Tate period in finite characteristic
    • to appear
    • J.-P. Allouche, D. Thakur, Automata and transcendence of Tate period in finite characteristic, Proc. Amer. Math. Soc., to appear.
    • Proc. Amer. Math. Soc.
    • Allouche, J.-P.1    Thakur, D.2
  • 11
    • 0010211187 scopus 로고
    • Hilbert series of fixed free algebras and noncommutative classical invariant theory
    • G. Almkvist, W. Dicks, E. Formanek, Hilbert series of fixed free algebras and noncommutative classical invariant theory, J. Algebra 93 (1985) 189-214.
    • (1985) J. Algebra , vol.93 , pp. 189-214
    • Almkvist, G.1    Dicks, W.2    Formanek, E.3
  • 12
    • 84966251385 scopus 로고
    • Growth functions for residually torsion-free nilpotents groups
    • R. C. Alperin, B. L. Peterson, Growth functions for residually torsion-free nilpotents groups, Proc. Amer. Math. Soc. 109 (1990) 585-587.
    • (1990) Proc. Amer. Math. Soc. , vol.109 , pp. 585-587
    • Alperin, R.C.1    Peterson, B.L.2
  • 13
    • 0023366701 scopus 로고
    • Prefixes of infinite words and ambiguous context-free languages
    • J.-M. Autebert, P. Flajolet, J. Gabarro, Prefixes of infinite words and ambiguous context-free languages, Inform. Process. Lett. 25 (1987) 211-216.
    • (1987) Inform. Process. Lett. , vol.25 , pp. 211-216
    • Autebert, J.-M.1    Flajolet, P.2    Gabarro, J.3
  • 14
    • 0003372863 scopus 로고    scopus 로고
    • Algorithmic number theory
    • MIT Press, Cambridge, MA
    • E. Bach, J. Shallit, Algorithmic number theory. Efficient Algorithms, vol. 1, MIT Press, Cambridge, MA; Series in the Foundations of Computing, The MIT Press, Cambridge MA, 1996 .
    • Efficient Algorithms , vol.1
    • Bach, E.1    Shallit, J.2
  • 15
    • 0347854094 scopus 로고    scopus 로고
    • The MIT Press, Cambridge MA
    • E. Bach, J. Shallit, Algorithmic number theory. Efficient Algorithms, vol. 1, MIT Press, Cambridge, MA; Series in the Foundations of Computing, The MIT Press, Cambridge MA, 1996 .
    • (1996) Series in the Foundations of Computing
  • 17
    • 0039894098 scopus 로고
    • Über Potenzreihen mit ganzzahligen Koeffizienten
    • F. Carlson, Über Potenzreihen mit ganzzahligen Koeffizienten, Math. Zeitschift 9 (1921) 1-13.
    • (1921) Math. Zeitschift , vol.9 , pp. 1-13
    • Carlson, F.1
  • 18
    • 77956972992 scopus 로고
    • The algebraic theory of context-free languages
    • P. Braffort, D. Hirschbert (Eds.), North-Holland, Amsterdam
    • N. Chomsky, M. P. Schützenberger, The algebraic theory of context-free languages, in: P. Braffort, D. Hirschbert (Eds.), Computer Programming and Formal Systems, North-Holland, Amsterdam, 1963, pp. 118-161.
    • (1963) Computer Programming and Formal Systems , pp. 118-161
    • Chomsky, N.1    Schützenberger, M.P.2
  • 19
    • 0001453259 scopus 로고
    • Ensembles presque périodiques k-reconnaissables
    • G. Christol, Ensembles presque périodiques k-reconnaissables, Theoret. Comput. Sci. 9 (1979) 141-145.
    • (1979) Theoret. Comput. Sci. , vol.9 , pp. 141-145
    • Christol, G.1
  • 21
    • 0000157608 scopus 로고
    • On the base-dependence of sets of numbers recognizable by finite automata
    • A. Cobham, On the base-dependence of sets of numbers recognizable by finite automata, Math. Systems Theory 3 (1969) 186-192.
    • (1969) Math. Systems Theory , vol.3 , pp. 186-192
    • Cobham, A.1
  • 22
    • 34249948426 scopus 로고
    • Uniform tag sequences
    • A. Cobham, Uniform tag sequences, Math. Systems Theory 6 (1972) 164-192.
    • (1972) Math. Systems Theory , vol.6 , pp. 164-192
    • Cobham, A.1
  • 23
    • 33748769984 scopus 로고
    • Abriß einer Theorie der höher Congruenzen in Bezug auf einen reellen Primzahl-Modulus
    • J.W.R. Dedekind, Abriß einer Theorie der höher Congruenzen in Bezug auf einen reellen Primzahl-Modulus, J. Reine Angew. Math. 54 (1857) 1-26. Reprinted in: R. Fricke, E. Noether, Ö. Ore (Eds.), Gesammelte mathematische Werke, Chelsea, New York, vol. 1, 1969, pp. 40-66.
    • (1857) J. Reine Angew. Math. , vol.54 , pp. 1-26
    • Dedekind, J.W.R.1
  • 24
    • 33748769984 scopus 로고
    • Chelsea, New York
    • J.W.R. Dedekind, Abriß einer Theorie der höher Congruenzen in Bezug auf einen reellen Primzahl- Modulus, J. Reine Angew. Math. 54 (1857) 1-26. Reprinted in: R. Fricke, E. Noether, Ö. Ore (Eds.), Gesammelte mathematische Werke, Chelsea, New York, vol. 1, 1969, pp. 40-66.
    • (1969) Gesammelte Mathematische Werke , vol.1 , pp. 40-66
    • Fricke, R.1    Noether, E.2    Ore, Ö.3
  • 25
    • 0013502531 scopus 로고
    • Transcendance du nombre de Thue-Morse
    • F. M. Dekking, Transcendance du nombre de Thue-Morse, C. R. Acad. Sci. Sér. I 285 (1977) 157-160.
    • (1977) C. R. Acad. Sci. Sér. I , vol.285 , pp. 157-160
    • Dekking, F.M.1
  • 28
    • 0001737037 scopus 로고
    • Séries trigonométriques et séries de Taylor
    • P. Fatou, Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906) 335-400.
    • (1906) Acta Math. , vol.30 , pp. 335-400
    • Fatou, P.1
  • 29
    • 0022319239 scopus 로고
    • Analytic models and ambiguity of context-free languages
    • P. Flajolet, Analytic models and ambiguity of context-free languages, Theoret. Comput. Sci. 49 (1987) 283-309.
    • (1987) Theoret. Comput. Sci. , vol.49 , pp. 283-309
    • Flajolet, P.1
  • 31
    • 0000543521 scopus 로고
    • Algebraic functions over finite fields
    • H. Furstenberg, Algebraic functions over finite fields, J. Algebra 7 (1967) 271-277.
    • (1967) J. Algebra , vol.7 , pp. 271-277
    • Furstenberg, H.1
  • 34
    • 85034558925 scopus 로고
    • Die Lehre von den Resten. II
    • H. Maser (Ed.), J. Springer, Berlin, reprinted by Chelsea, New York
    • C.F. Gauss, Die Lehre von den Resten. II, in: H. Maser (Ed.), Untersuchungen über höhere Arithmetik von Carl Friedrich Gauss, J. Springer, Berlin, 1889, pp. 602-629; reprinted by Chelsea, New York, 1981.
    • (1889) Untersuchungen Über Höhere Arithmetik von Carl Friedrich Gauss , pp. 602-629
    • Gauss, C.F.1
  • 35
    • 0030677012 scopus 로고    scopus 로고
    • On problems related to growth, entropy and spectrum in group theory
    • R. Grigorchuk, P. de la Harpe, On problems related to growth, entropy and spectrum in group theory, J. Dyn. Control Systems 3 (1997) 51-89.
    • (1997) J. Dyn. Control Systems , vol.3 , pp. 51-89
    • Grigorchuk, R.1    De La Harpe, P.2
  • 37
    • 51249170980 scopus 로고
    • Algebraic elements in formal power series rings
    • T. Harase, Algebraic elements in formal power series rings, Israel J. Math. 63 (1988) 281-288.
    • (1988) Israel J. Math. , vol.63 , pp. 281-288
    • Harase, T.1
  • 38
    • 0040665402 scopus 로고
    • Der Eisensteinsche Satz über Reihen-Entwicklung algebraischer Functionen
    • E. Heine, Der Eisensteinsche Satz über Reihen-Entwicklung algebraischer Functionen, J. Reine Angew. Math. 45 (1853) 285-302.
    • (1853) J. Reine Angew. Math. , vol.45 , pp. 285-302
    • Heine, E.1
  • 40
    • 85034556776 scopus 로고
    • Enumerating regular maps and normal subgroups of the modular group
    • V. Strehl (Ed.), Publication de l'IRMA, Strasbourg
    • e Séminaire Lotharingien de Combinatoire, 1986, Publication de l'IRMA, Strasbourg, pp. 81-88.
    • (1986) e Séminaire Lotharingien de Combinatoire , pp. 81-88
    • Jones, G.A.1
  • 41
    • 0004256326 scopus 로고
    • Classical Foundations and Multiplicative Groups, Marcel Dekker, New York
    • G. Karpilovsky, Field theory, Classical Foundations and Multiplicative Groups, Marcel Dekker, New York, 1988.
    • (1988) Field Theory
    • Karpilovsky, G.1
  • 42
    • 0002796533 scopus 로고
    • Sur les congruences des nombres eulériens et des coefficients différentiels des fonctions trigonométriques, suivant un module premier
    • E. Lucas, Sur les congruences des nombres eulériens et des coefficients différentiels des fonctions trigonométriques, suivant un module premier, Bull. Soc. Math. France 6 (1878) 49-54.
    • (1878) Bull. Soc. Math. France , vol.6 , pp. 49-54
    • Lucas, E.1
  • 43
    • 0000626948 scopus 로고
    • A generalization of a congruential property of Lucas
    • R.J. McIntosh, A generalization of a congruential property of Lucas, Amer. Math. Monthly 99 (1992) 231-238.
    • (1992) Amer. Math. Monthly , vol.99 , pp. 231-238
    • McIntosh, R.J.1
  • 44
    • 0001544807 scopus 로고
    • Dimension des courbes planes, papiers pliés et suites de Rudin-Shapiro
    • M. Mendès France, G. Tenenbaum, Dimension des courbes planes, papiers pliés et suites de Rudin-Shapiro, Bull. Soc. Math. France 109 (1981) 207-215.
    • (1981) Bull. Soc. Math. France , vol.109 , pp. 207-215
    • Mendès France, M.1    Tenenbaum, G.2
  • 47
    • 0002167683 scopus 로고    scopus 로고
    • 4-core partitions and class numbers
    • K. Ono, L. Sze, 4-core partitions and class numbers, Acta Arith. 80 (1997) 249-272.
    • (1997) Acta Arith. , vol.80 , pp. 249-272
    • Ono, K.1    Sze, L.2
  • 48
    • 0030182146 scopus 로고    scopus 로고
    • On the language of primitive words
    • H. Petersen, On the language of primitive words, Theoret. Comput. Sci. 161 (1996) 141-156.
    • (1996) Theoret. Comput. Sci. , vol.161 , pp. 141-156
    • Petersen, H.1
  • 49
    • 84973986431 scopus 로고
    • The divisibility of divisor functions
    • R.A. Rankin, The divisibility of divisor functions, Proc. Glasgow Math. Assoc. 5 (1961) 35-40.
    • (1961) Proc. Glasgow Math. Assoc. , vol.5 , pp. 35-40
    • Rankin, R.A.1
  • 50
    • 0009417104 scopus 로고
    • Mots circulaires et polynômes irréductibles
    • C. Reutenauer, Mots circulaires et polynômes irréductibles, Ann. Sci. Math. Québec 12 (1988) 275-285.
    • (1988) Ann. Sci. Math. Québec , vol.12 , pp. 275-285
    • Reutenauer, C.1
  • 51
    • 0000432807 scopus 로고
    • Finite automata and the set of squares
    • R.W. Ritchie, Finite automata and the set of squares, J. Assoc. Comput. Mach. 10 (1963) 528-531.
    • (1963) J. Assoc. Comput. Mach. , vol.10 , pp. 528-531
    • Ritchie, R.W.1
  • 52
    • 84941844239 scopus 로고
    • Über diejenigen Fälle in welchen die Gaussische hypergeometrische Reihe eine algebraische Funktion ihres vierten Elements darstellt
    • H.A. Schwarz, Über diejenigen Fälle in welchen die Gaussische hypergeometrische Reihe eine algebraische Funktion ihres vierten Elements darstellt, J. Reine Angew. Math. 75 (1872) 292-335.
    • (1872) J. Reine Angew. Math. , vol.75 , pp. 292-335
    • Schwarz, H.A.1
  • 54
    • 0040023457 scopus 로고
    • Children products of formal power series
    • H. Sharif, Children products of formal power series, Math. Japonica 38 (1993) 319-324.
    • (1993) Math. Japonica , vol.38 , pp. 319-324
    • Sharif, H.1
  • 55
    • 84963015776 scopus 로고
    • Algebraic functions over a field of positive characteristic
    • H. Sharif, C. F. Woodcock, Algebraic functions over a field of positive characteristic, J. London Math. Soc. 37 (1988) 395-403.
    • (1988) J. London Math. Soc. , vol.37 , pp. 395-403
    • Sharif, H.1    Woodcock, C.F.2
  • 56
    • 84968514104 scopus 로고
    • Differentiable dynamical systems
    • S. Smale, Differentiable dynamical systems, Bull. Am. Math. Soc. 73 (1967) 747-817.
    • (1967) Bull. Am. Math. Soc. , vol.73 , pp. 747-817
    • Smale, S.1
  • 57
    • 0347854035 scopus 로고
    • A four-dimensional Catalan formula
    • S.L. Snover, S.F. Troyer, A four-dimensional Catalan formula, Congr. Numer. 75 (1990) 123-126.
    • (1990) Congr. Numer. , vol.75 , pp. 123-126
    • Snover, S.L.1    Troyer, S.F.2
  • 58
    • 0000410641 scopus 로고
    • Differentiably finite power series
    • R.P. Stanley, Differentiably finite power series, European J. Comb. 1 (1980) 175-188.
    • (1980) European J. Comb. , vol.1 , pp. 175-188
    • Stanley, R.P.1
  • 59
    • 0039712772 scopus 로고    scopus 로고
    • Rational and transcendental growth series for the higher Heisenberg groups
    • M. Stoll, Rational and transcendental growth series for the higher Heisenberg groups, Invent. Math. 109 (1996) 85-109.
    • (1996) Invent. Math. , vol.109 , pp. 85-109
    • Stoll, M.1
  • 60
    • 0007148324 scopus 로고
    • Über Potenzreihen mit endlich vielen verschiedenen Koeffizienten, Sitzungsberichte der Preussischen Akademie der Wissenschaften
    • G. Szego, Über Potenzreihen mit endlich vielen verschiedenen Koeffizienten, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Phys.-Math. Klasse (1922) 88-91. Reprinted in Collected Papers, R. Askey (Ed.), Contemporary Mathematicians, vol. 1, Birkhäuser, Boston, 1982, pp. 557-561.
    • (1922) Phys.-Math. Klasse , pp. 88-91
    • Szego, G.1
  • 61
    • 85034563901 scopus 로고
    • Birkhäuser, Boston
    • G. Szego, Über Potenzreihen mit endlich vielen verschiedenen Koeffizienten, Sitzungsberichte der Preussischen Akademie der Wissenschaften, Phys.-Math. Klasse (1922) 88-91. Reprinted in Collected Papers, R. Askey (Ed.), Contemporary Mathematicians, vol. 1, Birkhäuser, Boston, 1982, pp. 557-561.
    • (1982) Contemporary Mathematicians , vol.1 , pp. 557-561
    • Askey, R.1
  • 62
    • 0003764203 scopus 로고
    • Institut Élie Cartan, Nancy
    • G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Institut Élie Cartan, Nancy, 1990; (see also G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory, Cambridge Studies in Advanced Mathematics, vol. 46, Cambridge Univ. Press, Cambridge, 1995, p. 165).
    • (1990) Introduction à la Théorie Analytique et Probabiliste des Nombres
    • Tenenbaum, G.1
  • 63
    • 0003244611 scopus 로고
    • Introduction to Analytic and Probabilistic Number Theory
    • Cambridge Univ. Press, Cambridge
    • G. Tenenbaum, Introduction à la théorie analytique et probabiliste des nombres, Institut Élie Cartan, Nancy, 1990; (see also G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory, Cambridge Studies in Advanced Mathematics, vol. 46, Cambridge Univ. Press, Cambridge, 1995, p. 165).
    • (1995) Cambridge Studies in Advanced Mathematics , vol.46 , pp. 165
    • Tenenbaum, G.1
  • 64
    • 17744361812 scopus 로고    scopus 로고
    • Exercices corrigés de théorie analytique et probabiliste des nombres
    • Société Mathématique de France, Paris
    • G. Tenenbaum, J. Wu, Exercices corrigés de théorie analytique et probabiliste des nombres, Cours spécialisés 2, Société Mathématique de France, Paris, 1996.
    • (1996) Cours Spécialisés , vol.2
    • Tenenbaum, G.1    Wu, J.2
  • 66
    • 38249022042 scopus 로고
    • On the transcendence of certain series
    • C.F. Woodcock, H. Sharif, On the transcendence of certain series, J. Algebra 121 (1989) 364-369.
    • (1989) J. Algebra , vol.121 , pp. 364-369
    • Woodcock, C.F.1    Sharif, H.2
  • 67
    • 0347223942 scopus 로고
    • Studien über die Bernoullischen und Eulerschen Zahlen
    • J. Worpitzky, Studien über die Bernoullischen und Eulerschen Zahlen, J. Reine Angew. Math. 94 (1881) 103-232.
    • (1881) J. Reine Angew. Math. , vol.94 , pp. 103-232
    • Worpitzky, J.1


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