ALGEBRAIC INDEPENDENCE OF CERTAIN MAHLER FUNCTIONS AND OF THEIR VALUES
2014 ◽
Vol 98
(3)
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pp. 289-310
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Keyword(s):
This paper considers algebraic independence and hypertranscendence of functions satisfying Mahler-type functional equations $af(z^{r})=f(z)+R(z)$, where $a$ is a nonzero complex number, $r$ an integer greater than 1, and $R(z)$ a rational function. Well-known results from the scope of Mahler’s method then imply algebraic independence over the rationals of the values of these functions at algebraic points. As an application, algebraic independence results on reciprocal sums of Fibonacci and Lucas numbers are obtained.
Keyword(s):
2016 ◽
Vol 12
(08)
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pp. 2159-2166
Keyword(s):
2014 ◽
Vol 43
(1)
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pp. 1-20
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Keyword(s):
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