Algebraic independence of certain power series of algebraic numbers
نویسندگان
چکیده
منابع مشابه
ALGEBRAIC INDEPENDENCE OF CERTAIN FORMAL POWER SERIES (I)
We give a proof of the generalisation of Mendes-France and Van der Poorten's recent result over an arbitrary field of positive characteristic and then by extending a result of Carlitz, we shall introduce a class of algebraically independent series.
متن کاملalgebraic independence of certain formal power series (i)
we give a proof of the generalisation of mendes-france and van der poorten's recent result over an arbitrary field of positive characteristic and then by extending a result of carlitz, we shall introduce a class of algebraically independent series.
متن کاملALGEBRAIC INDEPENENCE OF CERTAIN FORMAL POWER SERIES (II)
We shall extend the results of [5] and prove that if f = Z o a x ? Z [[X]] is algebraic over Q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over Q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over Q (x) if and only if f , f ,.., f are algebraically independent over Q (x)
متن کاملalgebraic indepenence of certain formal power series (ii)
we shall extend the results of [5] and prove that if f = z o a x ? z [[x]] is algebraic over q (x), where a = 1, ƒ 1 and if ? , ? ,..., ? are p-adic integers, then 1 ? , ? ,..., ? are linkarly independent over q if and only if (1+x) ,(1+x) ,…,(1+x) are algebraically independent over q (x) if and only if f , f ,.., f are algebraically independent over q (x)
متن کاملAlgebraic independence of some Lambert series
1] proved that if Y k0 (1 0 z F k) = X k0 "(k)z k ; then "(k) = 0 or 61 for any k 0. Tamura [7] generalized this result by proving the following theorem: Let fR k g k0 be a linear recurrence of positive integers satisfying R k+n = R k+n01 + 1 1 1 + R k (k 0) with n 2 and let P(z) = Y k0 (1 0 z R k) = X k0 "(k)z k : Then, if n is even, f"(k) j k 0g is a nite set; if in addition R k = 2 k (0 k n0...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1986
ISSN: 0022-314X
DOI: 10.1016/0022-314x(86)90080-6