Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hardy-Littlewood series and even continued fractions   For any $s\in (1/2,1]$, the series$F_s(x)=\sum_{n=1}^{\infty} e^{i\pi n^2
x}/n^s$ converges almost everywhere on $[-1,1]$ by a result of
Hardy-Littlewood, but not everywhere. However, there does not yet exist an
intrinsic description of the set of convergence for $F_s$. In this paper, we
define in terms of even or regular continued fractions certain subsets of
points of $[-1,1]$ of full measure where the series converges. Our method is
based on an approximate function equation for $F_s(x)$. As a by-product, we
obtain the convergence of certain series defined in term of the convergents of
the even continued fraction of an irrational number.

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The categories of this paper are: supr-con
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The categories of this paper are: stat
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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: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys