Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting zeros of Dedekind zeta functions   Given a number field $K$ of degree $n_K$ and with absolute discriminant
$d_K$, we obtain an explicit bound for the number $N_K(T)$ of non-trivial zeros
(counted with multiplicity), with height at most $T$, of the Dedekind zeta
function $\zeta_K(s)$ of $K$. More precisely, we show that for $T \geq 1$, $$
\Big| N_K (T) - \frac{T}{\pi} \log \Big( d_K \Big( \frac{T}{2\pi
e}\Big)^{n_K}\Big)\Big|
  \le 0.228 (\log d_K + n_K \log T) + 23.108 n_K + 4.520, $$ which improves
previous results of Kadiri and Ng, and Trudgian. The improvement is based on
ideas from the recent work of Bennett $et$ $al.$ on counting zeros of Dirichlet
$L$-functions.

5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
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The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
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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: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom