Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On balanced subgroups of the multiplicative group   A subgroup H of G=(Z/dZ)^* is called balanced if every coset of H is evenly
distributed between the lower and upper halves of G, i.e., has equal numbers of
elements with representatives in (0,d/2) and (d/2,d). This notion has
applications to ranks of elliptic curves. We give a simple criterion in terms
of characters for a subgroup H to be balanced, and for a fixed integer p, we
study the distribution of integers d such that the cyclic subgroup of (Z/dZ)^*
generated by p is balanced.

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The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
9
The categories of this paper are: nlin