Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transition Mean Values of Shifted Convolution Sums   Let f be a classical holomorphic cusp form for SL_2(Z) of weight k which is a
normalized eigenfunction for the Hecke algebra, and let \lambda(n) be its
eigenvalues. In this paper we study "shifted convolution sums" of the
eigenvalues \lambda(n) after averaging over many shifts h and obtain asymptotic
estimates. The result is somewhat surprising: one encounters a transition
region depending on the ratio of the square of the length of the average over h
to the length of the shifted convolution sum. The phenomenon is similar to that
encountered by Conrey, Farmer and Soundararajan in their 2000 paper Transition
Mean Values of Real Characters, and the connection of both results to
Eisenstein series and multiple Dirichlet series is discussed.

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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: hep-th
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The categories of this paper are: dg-ga
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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: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph