Algebraic independence of the values of power series, Lambert series, and infinite products generated by linear recurrences
Tanaka, Taka-aki
Osaka J. Math., Tome 42 (2005) no. 1, p. 487-497 / Harvested from Project Euclid
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In Theorem 1 of this paper, we establish the necessary and sufficient condition for the values of a power series, a Lambert series, and an infinite product generated by a linear recurrence at the same set of algebraic points to be algebraically dependent. In Theorem 4, from which Theorems 1--3 are deduced, we obtain an easily confirmable condition under which the values more general than those considered in Theorem 1 are algebraically independent, improving the method of [5].
Publié le : 2005-06-14
Classification:  
@article{1153494390,
     author = {Tanaka, Taka-aki},
     title = {Algebraic independence of the values of power series, Lambert series, and infinite products generated by linear recurrences},
     journal = {Osaka J. Math.},
     volume = {42},
     number = {1},
     year = {2005},
     pages = { 487-497},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1153494390}
}

Tanaka, Taka-aki. Algebraic independence of the values of power series, Lambert series, and infinite products generated by linear recurrences. Osaka J. Math., Tome 42 (2005) no. 1, pp.  487-497. http://gdmltest.u-ga.fr/item/1153494390/