On infinite products associated with sums of digits
نویسندگان
چکیده
منابع مشابه
Infinite Sums, Infinite Products, and ζ(2k)
The most basic concept is that of an infinite sequence (of real or complex numbers in these notes). For p ∈ Z, let Np = {k ∈ Z : k ≥ p}. An infinite sequence of (complex) numbers is a function a : Np → C. Usually, for n ∈ Np we write a(n) = an, and denote the sequence by a = {an}n=p. The sequence {an}n=p is said to converge to the limit A ∈ C provided that for each > 0 there is an N ∈ Z such th...
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Let denote the sum of the digits in the baserepresentation of . In a celebrated paper, Thue showed that the infinite word is overlap-free, i.e., contains no subword of the form , where is any finite word and is a single symbol. Let "! be integers with $#% , !&#(' . In this paper, generalizing Thue’s result, we prove that the infinite word ) +* ,./. 0 1 2!3 is overlap-free if and only if !4#5 . ...
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In this paper we investigate the infinite convergent sum T = ∑∞ n=0 P (n) Q(n) , where P (x) ∈ Q[x], Q(x) ∈ Q[x] and Q(x) has only simple rational zeros. N. Saradha and R. Tijdeman have obtained sufficient and necessary conditions for the transcendence of T if the degree of Q(x) is 3. In this paper we give sufficient and necessary conditions for the transcendence of T if the degree of Q(x) is 4...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1985
ISSN: 0022-314X
DOI: 10.1016/0022-314x(85)90045-9