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Algebraic independence of the values at algebraic points of a class of functions considered by Mahler

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Seria
Rozprawy Matematyczne tom/nr w serii: 303 wydano: 1990
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Warianty tytułu
Abstrakty
EN

CONTENTS
Acknowledgements...................................................................4
I. Introduction
§ 1.1. Algebraic independence.................................................5
§ 1.2. Notation and some estimates..........................................9
II. Formal series
§ 2.1. A class to which the solution belong..............................11
III. Zero estimates.
§ 3.1. The general case ........................................................15
§ 3.2. Resultants.....................................................................23
§ 3.3. The upper triangular case ...........................................26
IV. Preliminaries
§ 4.1. Ideals............................................................................30
§ 4.2. Some lemmas ..............................................................34
V. The main results
§ 5.1. Hypothesis Hyp(f,α)......................................................41
§ 5.2. Conclusions .................................................................45
Appendix.................................................................................53
References.............................................................................60
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 303
Liczba stron
61
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCIII
Daty
wydano
1990
Twórcy
autor
  • Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1003, U.S.A.
  • 57 Arapito Rd, Titirangi, Auckland 7, New Zealand
Bibliografia
  • [В] P.-G. Becker-Landeck, Maße für algebraische Unabhängigkeit nach einer Methode von Mahler, Acta Arith. 50 (1988), 279-293.
  • [Br] W. D. Brownawell, Effectively in independence measures for values of E-functions, J. Austral. Math. Soc. Ser. 39 (1985), 227-240.
  • [Ch] G. Chudnovsky, Contributions to the Theory of Transcendental Numbers, Surveys and Monographs, 19, AMS, 1984.
  • [G] A. I. Galochkin, A transcendence measure for the values of functions satisfying certain functional equations, Mat. Zametki 27 (1980), 175-183; English transl. in Math. Notes 27 (1980).
  • [K] К. K. Kubota, On the algebraic independence of holomorphic solutions of certain functional equations and their values, Math. Ann. 227 (1970), 9-50.
  • [La1] S. Lang, Introduction to Transcendental Numbers, Addison-Wesley, 1966.
  • [La2] S. Lang, A transcndence measure for E-functions, Mathematika 9 (1962), 157-161.
  • [L] J. H. Loxton, Automata and Transcendence, Chapter 13 of: New Advances in Transcendence Theory, A. Baker (ed.), Cambridge Univ. Press, 1988.
  • [LP1] J. H. Loxton and A. J. van der Poorten, Algebraic independence properties of the Fredholm series, J. Austral. Math. Soc. Ser. A 26 (1978), 31-45.
  • [LP2] J. H. Loxton and A. J. van der Poorten, Arithmetic properties of certain functions in several variables III, Bull. Austral. Math. Soc. 16 (1977), 15-47.
  • [LP3] J. H. Loxton and A. J. van der Poorten, A class f hypertranscendental functions, Aequationes Math. 16 (1977), 93-106.
  • [Ma1] K. Mahler, Remarks on a paper by W. Schwarz, J. Number Theory 1 (1969), 512-521.
  • [Ma2] K. Mahler, Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen, Math. Ann. 101 (1929), 342-366.
  • [Ma3] K. Mahler, Arithmetische Eigenschaften einer Klasse transzendental-transzendenter Funktionen, Math. Z. 32 (1930), 545-585.
  • [Ma4] K. Mahler, Über das Verschwinden von Potenzreihen mehrerer Veränderlichen in speziellen Punktfolgen, Math. Ann. 103 (1930), 573-587.
  • [M1] W. Miller, Transcendence measures for values of analytic solutions to certain functional equations, Ph. D. Thesis, University of Michigan 1979.
  • [M2] W. Miller, Transcendence measures by a method of Mahler, J. Austral. Math. Soc. Ser. A 32 (1982), 68-72.
  • [Ne1] Yu. V. Nesterenko, Estimates for the orders of zeros of functions of a certain class and applications in the theory of transcendental numbers, Izv. Akad. Nauk SSSR Ser. Mat. 41 (1977), 253-284; English transl. in Math. USSR-Izv. 11 (1977).
  • [Ne2] Yu. V. Nesterenko, Estimates for the characteristic function of a prime ideal, Mat. Sb. 123 (165)
  • (1984), 11-49; English transl. in Math. USSR-Sb. 51 (1) (1985).
  • [Ne3] Yu. V. Nesterenko, On algebraic independence of algebraic powers of algebraic numbers, Mat. Sb. 123 (165) (1984), 435-459; English transl. in Math. USSR-Sb. 51 (1985).
  • [Ne4] Yu. V. Nesterenko, On a measure of the algebraic independence of the values of certain functions, Mat. Sb. 128 (170) (1985), 545-568; English transl. in Math. USSR-Sb. 56 (2) (1987).
  • [Sh] A. V. Shidlovskiĭ, On criteria for algebraic independence of a class of entire functions, Izv. Akad. Nauk SSSR Ser. Mat. 23 (1959), 35-66; English transl. in Amer. Math. Soc. Transl. (2) 22 (1962).
  • [Sie] C. L. Siegel, Approximation algebraischer Zahlen, Math. Z. 10 (1921), 173-213.
  • [Wae] B. L. van der Waerden, Modern Algebra, Vols. 1 and 2, F. Ungar, New York 1950 and 1953.
  • [Wa] M. Waldschmidt, Nombres Transcendants, Springer, Berlin-New York 1974.
Języki publikacji
EN
Uwagi
1985 Mathematics Subject Classification 11J85
Identyfikator YADDA
bwmeta1.element.zamlynska-1a3fe28d-93d7-41af-a702-4b185ee0fe85
Identyfikatory
ISBN
83-85116-02-8
ISSN
0012-3862
Kolekcja
DML-PL
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