Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the distribution of the order and index for the reductions of
  algebraic numbers   Let $\alpha_1,\ldots,\alpha_r$ be algebraic numbers in a number field $K$
generating a subgroup of rank $r$ in $K^\times$. We investigate under GRH the
number of primes $\mathfrak p$ of $K$ such that each of the orders of
$(\alpha_i\bmod\mathfrak p)$ lies in a given arithmetic progression associated
to $\alpha_i$. We also study the primes $\mathfrak p$ for which the index of
$(\alpha_i\bmod\mathfrak p)$ is a fixed integer or lies in a given set of
integers for each $i$. An additional condition on the Frobenius conjugacy class
of $\mathfrak p$ may be considered. Such results are generalizations of a
theorem of Ziegler from 2006, which concerns the case $r=1$ of this problem.

34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph