Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds for the first several prime character nonresidues   Let $\varepsilon > 0$. We prove that there are constants
$m_0=m_0(\varepsilon)$ and $\kappa=\kappa(\varepsilon) > 0$ for which the
following holds: For every integer $m > m_0$ and every nontrivial Dirichlet
character modulo $m$, there are more than $m^{\kappa}$ primes $\ell \le
m^{\frac{1}{4\sqrt{e}}+\varepsilon}$ with $\chi(\ell)\notin \{0,1\}$. The proof
uses the fundamental lemma of the sieve, Norton's refinement of the Burgess
bounds, and a result of Tenenbaum on the distribution of smooth numbers
satisfying a coprimality condition. For quadratic characters, we demonstrate a
somewhat weaker lower bound on the number of primes $\ell \le
m^{\frac14+\epsilon}$ with $\chi(\ell)=1$.

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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat