Linear independence results for sums of reciprocals of Fibonacci and Lucas numbers.

The aim of this paper is to give linear independence results for the values of Lambert type series. As an application, we derive arithmetical properties of the sums of reciprocals of Fibonacci and Lucas numbers associated with certain coprime sequences { n ℓ } ℓ ≥ 1 . For example, the three numbers 1 , ∑ p : prime 1 F p 2 , ∑ p : prime 1 L p 2 are linearly independent over Q (5) , where { F n } and { L n } are the Fibonacci and Lucas numbers, respectively. [ABSTRACT FROM AUTHOR]