Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the meromorphic continuation of Beatty Zeta-Functions and Sturmian
  Dirichlet series   For a positive irrational number $\alpha,$ we study the ordinary Dirichlet
series $\zeta_\alpha(s) = \sum\limits_{n\geq1} \lfloor\alpha n\rfloor^{-s}$ and
$S_\alpha(s) = \sum\limits_{n\geq1} (\left\lceil\alpha n\right\rceil -
\left\lceil \alpha (n-1)\right\rceil){n^{-s}}.$ We prove relations between them
and $J_{\boldsymbol{\alpha}}(s)=\sum\limits_{n\geq1}\left(\lbrace\alpha
n\rbrace-\frac{1}{2}\right)n^{-s}.$ Motivated by the previous work of Hardy and
Littlewood, Hecke and others regarding $J_{\boldsymbol{\alpha}},$ we show that
$\zeta_\alpha$ and $S_\alpha$ can be continued analytically beyond the
imaginary axis except for a simple pole at $s=1.$ Based on the latter results,
we also prove that the series
$\zeta_{\alpha}(s;\beta)=\sum\limits_{n\geq0}\left(\lfloor\alpha
n\rfloor+\beta\right)^{-s}$ can be continued analytically beyond the imaginary
axis except for a simple pole at $s=1.$

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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: stat
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org