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An Investigation on P-Adic U Numbers

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Abstract (2. Language): 
In this paper, firstly we show that there are infinitely many p-adic numbers y such that y E UIr1 and P, ( y ) E Ulr1 where k E N , 1 < i < k and P, (x) are non-constant polynomials with integer coefficients. Secondly, we prove that the finite linear combination of p-adic algebraic numbers and semi-strong p-adic U-numbers belong to A u U . Finally, we prove that if y is a p-adic U-number and y is a semi-strong p-adic U-number, then both y + y and y . y numbers belong to A u U . Moreover, we remark that if y is taken as a p-adic U-number the last statement fails to be true.

REFERENCES

References: 

[I] (1992) ALNIACIK, K. On semi-strong U-numbers. Acta Aritmatica LX.4, 349 -
358.
[2] (1998) ALNIACIK, K. The points on curves whose coordinates are U-numbers.
Rendiconti di Matematica Serie VII Vo. 18 , 649 - 653.
[3] (1991) ALNIACIK, K. On p-Adic I/,,,-Numbers. Istanbul ~ nFe.n Fak. Mat. Der.
50, 1 - 17.
[4] (1996) DURU, H. On Semi-strong p-Adic U-Numbers. (to appear in Istanbul ~ n .
Fen Fak. Mat. Der.
[5] ( ~ ~ ~ ~ ) E R D Po. s R, epresentation of real numbers as sums and products of
Liouville numbers. Michigan Math. J. 9, 59 - 60.
[6] (1973) ICEN, 0.9. Anhang zu den Arbeiten " ~ b e rd ie Funktionswerte der padisch
elliptischen Funktionen I und II". Revue de la Fac. de Sci, de I'Universite d'
Istanbul, Ser. A 8, 25 - 35.
[7] (1939) KOKSMA, J.F. ~ b e drie Mahlersche Klasseneinteilung der transzendenten
Zahlen und die Approximation komplexer durch algebraische Zahlen.
Monatshefte Math. Physik 48, 176 - 189.
[8] (1953) LEVEQUE, W.J. On Mahler's U- Numbers. London Math. Soc., 220 -
229.
[9] (1989) LONG, X.X. Mahler's Classification of p-Adic Numbers. Pure Apply,
Math. 5,73 - 80.
[lo] (1932) MAHLER, K. Zur Approximation der Exponentialfunktion und des
Logarithmus I. J. Reine Angew. Math. 166, 137 - 150.
[11] (1935) MAHLER, K. ~ b e rei ne Klassen-Einteilung der p-adischen Zahlen.
Mathematica (Leiden) 3, 177 - 185.
[12] (1934) MORRISON, J.F. Approximation of p-Adic Numbers By Algebraic
Numbers of Bounded Degree. Journal of Number Theory 10,334 - 350.
[13] (1981) SCHLICKEWEI, H.P. p-Adic T-Numbers Do Exist. Acta Aritmatica
XXXIX, 181 - 191.
[14] (1960) WIRSING. E. Approximation mit Algebraischen Zahlen Beschrankten
Grades. J. Reine Angew. Math. 206,67 - 77.

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