Some Generalized Lacunary Power Series with Algebraic Coefficients for Mahler’s U−number Arguments
نویسنده
چکیده
In this work, we show that under certain conditions the values of some generalized lacunary power series with algebraic coefficients for Mahler’s Um−number arguments belong to either a certain algebraic number field or ⋃t i=1 Ui in Mahler’s classification of the complex numbers, where t denotes a positive rational integer dependent on the coefficients of the given series and on the argument. Moreover, the obtained results are adapted to the fieldQp of p−adic numbers.
منابع مشابه
Auxiliary Polynomials for Some Problems regarding Mahler’s Measure
We describe an iterative method of constructing some favorable auxiliary polynomials used to obtain lower bounds in some problems of algebraic number theory. With this method we improve a lower bound on Mahler’s measure of a polynomial with no cyclotomic factors whose coefficients are all congruent to 1 modulo m for some integer m ≥ 2, raise a lower bound in the problem of Schinzel and Zassenha...
متن کاملAnother proof of Soittola's theorem
Soittola’s theorem characterizes R+or N-rational formal power series in one variable among the rational formal power series with nonnegative coefficients. We present here a new proof of the theorem based on Soittola’s and Perrin’s proofs together with some new ideas that allows us to separate algebraic and analytic arguments. c © 2008 Elsevier B.V. All rights reserved.
متن کاملAlgebraic independence results on the generating Lambert series of the powers of a fixed integer
In this paper, the algebraic independence of values of the functionGd(z) := ∑ h≥0 z dh/(1− zdh ), d>1 a fixed integer, at non-zero algebraic points in the unit disk is studied. Whereas the case of multiplicatively independent points has been resolved some time ago, a particularly interesting case of multiplicatively dependent points is considered here, and similar results are obtained for more ...
متن کاملAlgebraic Generalized Power Series and Automata
A theorem of Christol states that a power series over a finite field is algebraic over the polynomial ring if and only if its coefficients can be generated by a finite automaton. Using Christol’s result, we prove that the same assertion holds for generalized power series (whose index sets may be arbitrary well-ordered sets of nonnegative rationals).
متن کاملHYPERTRANSCENDENTAL FORMAL POWER SERIES OVER FIELDS OF POSITIVE CHARACTERISTIC
Let $K$ be a field of characteristic$p>0$, $K[[x]]$, the ring of formal power series over $ K$,$K((x))$, the quotient field of $ K[[x]]$, and $ K(x)$ the fieldof rational functions over $K$. We shall give somecharacterizations of an algebraic function $fin K((x))$ over $K$.Let $L$ be a field of characteristic zero. The power series $finL[[x]]$ is called differentially algebraic, if it satisfies...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013