Algebraic independence results related to linear recurrences
Taka Aki Tanaka · Osaka City University (Osaka City University) · 1999
this paper we shall overcome this difficulty by considering a generic point of an irreducible algebraic variety. Theorems 1 and 2 in this paper assert that certain types of functional equations in several variables have no nontrivial rational function solutions. As applications, we shall prove the algebraic independence of various kinds of reciprocal sums of linear recurrences in Theorems 3 and 4, and that of the values at algebraic numbers of power series, Lambert series, and infinite products generated by linear recurrences in Theorem 5. Let \\Omega = (! ij ) be an n 2 n matrix with nonnegative integer entries. If