Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Low-lying zeros of elliptic curve L-functions: Beyond the ratios
  conjecture   We study the low-lying zeros of L-functions attached to quadratic twists of a
given elliptic curve E defined over $\mathbb Q$. We are primarily interested in
the family of all twists coprime to the conductor of E and compute a very
precise expression for the corresponding 1-level density. In particular, for
test functions whose Fourier transforms have sufficiently restricted support,
we are able to compute the 1-level density up to an error term that is
significantly sharper than the square-root error term predicted by the
L-functions Ratios Conjecture.

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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc