Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elliptic curves of unbounded rank and Chebyshev's bias   We establish a conditional equivalence between quantitative unboundedness of
the analytic rank of elliptic curves over $\mathbb Q$ and the existence of
highly biased elliptic curve prime number races. We show that conditionally on
a Riemann Hypothesis and on a hypothesis on the multiplicity of the zeros of
$L(E,s)$, large analytic ranks translate into an extreme Chebyshev bias.
Conversely, we show under a certain linear independence hypothesis on zeros of
$L(E,s)$ that if highly biased elliptic curve prime number races do exist, then
the Riemann Hypothesis holds for infinitely many elliptic curve $L$-functions
and there exist elliptic curves of arbitrarily large rank.

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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an