Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On sum of Hecke eigenvalue squares over primes in very short intervals   Let $\eta>0$ be a fixed positive number, let $N$ be a sufficiently large
number. In this paper, we study the second moment of the sum of Hecke
eigenvalues over primes in short intervals (whose length is $\eta \log N$) on
average (with some weights) over the family of weight $k$ holomorphic Hecke
cusp forms. We also generalize the above result to Hecke-Maass cusp forms for
$SL(2,\mathbb{Z})$ and $SL(3,\mathbb{Z}).$ By applying the Hardy-Littlewood
prime 2-tuples conjecture, we calculate the exact values of the mean values.

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The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
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The categories of this paper are: q-fin
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The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio