Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the coefficients of symmetric power $L$-functions   We study the signs of the Fourier coefficients of a newform. Let $f$ be a
normalized newform of weight $k$ for $\Gamma_0(N)$. Let $a_f(n)$ be the $n$th
Fourier coefficient of $f$. For any fixed positive integer $m$, we study the
distribution of the signs of $\{a_f(p^m)\}_p$, where $p$ runs over all prime
numbers. We also find out the abscissas of absolute convergence of two
Dirichlet series with coefficients involving the Fourier coefficients of cusp
forms and the coefficients of symmetric power $L$-functions.

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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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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: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn