Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Riemann's Zeta Function: The alternating Xi-Function Xia(s)   As well known, the study of Riemanns zeta function {\zeta}(s) involves the
related entire function {\xi}(s). A close relative of {\zeta}(s) is the
alternating zeta function {\eta}(s). Similar to {\zeta}(s), also {\eta}(s) has
a corresponding entire function {\xi}_a (s). After establishing its definition
and a related functional equation, formulas based on incomplete gamma functions
are worked out, allowing to numerically evaluate {\xi}_a (s). Examples
verifying the obtained formulas are included.

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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph