On the meromorphic continuation of Beatty Zeta-functions and Sturmian Dirichlet series

@inproceedings{Sourmelidis2018OnTM,
  title={On the meromorphic continuation of Beatty Zeta-functions and Sturmian Dirichlet series},
  author={Athanasios Sourmelidis},
  year={2018}
}
Abstract For a positive irrational number α, we study the ordinary Dirichlet series ζ α ( s ) = ∑ n ≥ 1 ⌊ α n ⌋ − s and S α ( s ) = ∑ n ≥ 1 ( ⌈ α n ⌉ − ⌈ α ( n − 1 ) ⌉ ) n − s . We prove relations between them and J α ( s ) = ∑ n ≥ 1 ( { α n } − 1 2 ) n − s . Motivated by the previous work of Hardy and Littlewood, Hecke and others regarding J α , we show that ζ α and S α can be continued analytically beyond the imaginary axis except for a simple pole at s = 1 . Based on the latter results, we… CONTINUE READING
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