Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Sato-Tate conjecture and Nagao's conjecture   Nagao's conjecture relates the rank of an elliptic surface to a limit formula
arising from a weighted average of fibral Frobenius traces, and it is further
generalized for smooth irreducible projective surfaces by M. Hindry and A.
Pacheco. We show that the Sato-Tate conjecture based on the random matrix model
implies Nagao's conjecture for certain twist families of elliptic curves and
hyperelliptic curves.

9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
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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: acc-phys