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ARITHMETICAL PROPERTIES OF THE VALUES OF SOME POWER SERIES WITH ALGEBRAIC COEFFICIENTS TAKEN FOR f/m-NUMBERS ARGUMENTS.

Journal Name:

  • İstanbul Üniversitesi Fen Fakültesi Matematik, Fizik ve Astronomi Dergisi

Publication Year:

  • 1996-1997
Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In this paper it is proved that the values of some gap series for Um-numbers arguments are either a (/-number of degree < m or an element of a certain algebraic number field. In this work the method which is used by Oryan for Liouville numbers in [9] and [10] is extended to the Um-numbers. This extended method is used first for the gap series with rational coefficients and then for the gap series with algebraic coefficients. Further by using the similar methods for the p-adic gap series the similar results are obtained. The obtained results in the work contains the theorems in [9], [10] as special cases.
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  • English

REFERENCES

References: 

[1]
BAKER
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[2] İÇEN, O.Ş. :
Anhang zu den Arbeiten "Uber die Funktionswerte der p-adischen elliptischen Funktionen I und II", İst. Üniv. Fen Fak. Mee. Seri A, 38 (1973), 25-35.
[3] KOKSMA, J.F. :
Uber die Mahlersche Klasseneinteilung der transzendenten Zahlen und die Approximation komplexer Zahlen durch algebraische Zahlen, Monatsh. Math. Physik, 48 (1939), 176-189.
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LeVEQUE
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MAHLER
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Approximation
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[8] ORYAN,
M.H.
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Uber gewisse Potenzreihen, die für algebraische Argumente Werte aus den Mahlerschen Unterklassen Um nehmen, Ist. Üniv. Fen Fak. Mee. Seri A, 45 (1980), 1-42.
[9] ORYAN, M.H. :
Uber gewisse Potenzreihen, deren Funktionswerte für Argumente aus der Menge der p-adischen Liouvilleschen Zahlen p-adische V'-Zahlen vom Grade < m sind, İst. Üniv. Fen Fak. Mee. Seri A, 47 (1983-1986), 53-67.
[10] ORYAN, M.H. :
On the Power Series and Liouville Numbers, Doğa Tr. J. of Mathematics, 14 (1990), 79-90.
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[11] SCHNEIDER, Th. : Einführung in die transzendenten Zahlen, Berlin, Göttingen, Heidelberg, 1957.
[12] WIRSING, E. : Approximation mit algebraischen Zahlen beschränkten Grades, J. Reine Angew. Math., 206 (1961), 67-77.
[13] ZEREN, B.M. : Uber einige komplexe und p-adische Lückenreihen mit Werten aus der Mahlerschen Unterklassen £7m, Ist. Univ. Fen Fak. Mec. Seri A. 45 (1980), 89-130.

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