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Journals / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 5

On the values of some generalized lacunary power series wıth algebraic coefficients for Liouville number arguments

Gülcan KEKEÇ
Pages
691–702
Publication Date
2022-10-18
DOI
—
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⚡ TL;DR(Too Long; Didn't Read)

In this work, it is shown that under certain conditions, the values of some generalized lacunary power series with algebraic coefficients from a certain algebraic number field K of degree m for Liouville number arguments belong to either the algebraic number field K or$U^m{_i=1}{U_i}$ Mahler’s classification of the complex numbers.

📌 3 Key Takeaways

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Objective & Hypothesis:In this work, it is shown that under certain conditions, the values of some generalized lacunary power series with algebraic coefficients from a certain algebraic number field K of degree m for Liouville number arguments belong to either the algebraic number field K or$U^m{_i=1}{U_i}$ Mahler’s classification of the complex numbers.
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Key Findings & Data:In this work, it is shown that under certain conditions, the values of some generalized lacunary power series with algebraic coefficients from a certain algebraic number field K of degree m for Liouville number arguments belong to either the algebraic number field K or$U^m{_i=1}{U_i}$ Mahler’s classification of the complex numbers.
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Conclusion & Impact:In this work, it is shown that under certain conditions, the values of some generalized lacunary power series with algebraic coefficients from a certain algebraic number field K of degree m for Liouville number arguments belong to either the algebraic number field K or$U^m{_i=1}{U_i}$ Mahler’s classification of the complex numbers.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this work, it is shown that under certain conditions, the values of some generalized lacunary power series with algebraic coefficients from a certain algebraic number field K of degree m for Liouville number arguments belong to either the algebraic number field K or$U^m{_i=1}{U_i}$ Mahler’s classification of the complex numbers.

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Cite This Article

KEKEÇ, G. (2022). On the values of some generalized lacunary power series wıth algebraic coefficients for Liouville number arguments. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 5, 691–702. https://ajindex.com/articles/530568

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References (14)

  1. Braune, E.Über arithmetische Eigenschaften von Lückenreihen mit algebraischen Koeffizienten und algebraischem Argument, Monatsh. Math. 84, 1–11, 1977
  2. Cohn, H. Note on almost algebraic numbers, Bull. Amer. Math. Soc. 52, 1042–1045, 1946. [3]İçen, O. S¸. Anhang zu den Arbeiten ”¨Uber die Funktionswerte der p-adisch elliptischen Funktionen. I, II”, İstanbul Üniv. Fen Fak. Mecm. Ser. A 38, 25–35, 1973
  3. Kekeç, G. On some Lacunary power series with algebraic coefficients for Liouville number arguments, İstanb. Üniv. Fen Fak. Mat. Fiz. Astron. Derg. (N. S.) 3, 15–32, 2008/09
  4. Koksma, J.F. Über die Mahlersche Klasseneinteilung der transzendenten Zahlen und die Approximation komplexer Zahlen durch algebraische Zahlen, Monatsh. Math. Phys. 48,176–189, 1939
  5. LeVeque, W. J. On Mahler’s U-numbers, J. London Math. Soc. 28, 220–229, 1953
  6. LeVeque, W. J. Topics in Number Theory Volume II (Addison-Wesley Publishing, London,1961)
  7. Mahler, K. Zur Approximation der Exponentialfunktion und des Logarithmus. I, II, J. Reine Angew. Math. 166, 118–150, 1932
  8. Mahler, K. Arithmetic properties of lacunary power series with integral coefficients, J. Austral.Math. Soc. 5, 56–64, 1965
  9. Perron, O. Irrationalzahlen (Walter de Gruyter & Co., Berlin, 1960)
  10. Schneider, T. Einführung in die transzendenten Zahlen (Springer-Verlag, Berlin-Göttingen-Heidelberg, 1957)
  11. Wirsing, E. Approximation mit algebraischen Zahlen beschrankten Grades, J. Reine Angew. Math. 206, 67–77, 1961
  12. Yılmaz, G. On the gap series and Liouville numbers, İstanbul Üniv. Fen Fak. Mat. Derg. 60, 111–116, 2001
  13. Zeren, B.M. Über einige komplexe und p-adische Lückenreihen mit Werten aus den Mahlerschen Unterklassen Um, İstanbul ¨Univ. Fen Fak. Mecm. Ser. A 45, 89–130, 1980
  14. Zeren, B.M. ¨Uber die Natur der Transzendenz der Werte einer Art verallgemeinerter Lückenreihen mit algebraischen Koeffizienten für algebraische Argumente, İstanbul Tek. Üniv.Bül. 41, 569–588, 1988.