Linear independence of certain Lambert series
نویسندگان
چکیده
منابع مشابه
Algebraic 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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In this note we investigate arithmetic properties of values of the Tschakaloff function Tq(z) = P∞ ν=0 q −ν(ν+1)/2zν , |q| > 1. One of the open problems is proving linear independence of the values of Tq(z) with different q. The only result obtained in this direction in [1] is very restrictive. We refer an interested reader to the survey [2] for an account of known linear and algebraic independ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2014
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2014-12102-2