Sums involving 1/sin^σ terms over Fibonacci ratios asymptote to C n + D plus exponentially small error for σ>1, with constants from Dedekind zeta of Q(√5), and admit closed forms in special cases.
Some results on generalized Fibonacci and Lucas numbers and Dedekind sums.Fibonacci Quart., 42(3):250–255, 2004
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Precise Asymptotics and Exact Formulas for Tensor Product Energies of Fibonacci Lattices
Sums involving 1/sin^σ terms over Fibonacci ratios asymptote to C n + D plus exponentially small error for σ>1, with constants from Dedekind zeta of Q(√5), and admit closed forms in special cases.