Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recurrence relations for Mellin transforms of $GL(n,\mathbb{R})$
  Whittaker functions   Using a recursive formula for the Mellin transform $T_{n,a}(s)$ of a
spherical, principal series $GL(n,\mathbb{R})$ Whittaker function, we develop
an explicit recurrence relation for this Mellin transform. This relation, for
any $n\ge2$, expresses $T_{n,a}(s)$ in terms of a number of "shifted"
transforms $T_{n,a}(s+\Sigma)$, with each coordinate of $\Sigma$ being a
non-negative integer.
  We then focus on the case $n=4$. In this case, we use the relation referenced
above to derive further relations, each of which involves "strictly positive
shifts" in one of the coordinates of $s$. More specifically: each of our new
relations expresses $T_{4,a}(s)$ in terms of $T_{4,a}(s+\Sigma)$ and
$T_{4,a}(s+\Omega)$, where for some $1\le k\le 3$, the $k$th coordinates of
both $\Sigma$ and $\Omega$ are strictly positive.
  Finally, we deduce a recurrence relation for $T_{4,a}(s)$ involving strictly
positive shifts in all three $s_k$'s at once. (That is, the condition "for some
$1\le k\le 3$" above becomes "for all $1\le k\le 3$.")
  These additional relations on $GL(4,\mathbb{R})$ may be applied to the
explicit understanding of certain poles and residues of $T_{4,a}(s)$. This
residue information is, as we describe below, in turn relevant to work of
Goldfeld and Woodbury, concerning orthogonality of Fourier coefficients of
$SL(4,\mathbb{R})$ Maass forms, and the $GL(4)$ Kuznetsov formula.

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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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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: funct-an