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On Linear Relations For Dirichlet Series Formed By Recursive Sequences Of Second Order
Let Fn and Ln be the Fibonacci and Lucas numbers, respectively. Four corresponding zeta functions in s are defined by
ζF(s):=∑n=1∞1Fsn,ζ∗F(s):=∑n=1∞(−1)n+1Fsn,ζL(s):=∑n=1∞1Lsn,ζ∗L(s):=∑n=1∞(−1)n+1Lsn.
As a consequence of Nesterenko’s proof of the algebraic independence of the three Ramanujan functions R(ρ),Q(ρ), and P(ρ) for any algebraic number ρ with 0
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