Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Motohashi's Formula for the Fourth Moment of Individual Dirichlet
  $L$-Functions and Applications   A new reciprocity formula for Dirichlet $L$-functions associated to an
arbitrary primitive Dirichlet character of prime modulus $q$ is established. We
find an identity relating the fourth moment of individual Dirichlet
$L$-functions in the $t$-aspect to the cubic moment of central $L$-values of
Hecke-Maass newforms of level at most $q^{2}$ and primitive central character
$\psi^{2}$ averaged over all primitive nonquadratic characters $\psi$ modulo
$q$. Our formulae would be viewed as reverse versions of recent work of
Petrow-Young. Direct corollaries include a version of Iwaniec's short interval
fourth moment bound and the twelfth moment bound for individual Dirichlet
$L$-functions, which generalise work of Jutila and Jutila-Motohashi,
respectively. This work traverses an intersection of analytic number theory and
automorphic forms.

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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: patt-sol