Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elliptic aliquot cycles of fixed length   Silverman and Stange define the notion of an aliquot cycle of length L for a
fixed elliptic curve E defined over the rational numbers, and conjecture an
order of magnitude for the function which counts such aliquot cycles. In the
present note, we combine heuristics of Lang-Trotter with those of Koblitz to
refine their conjecture to a precise asymptotic formula by specifying the
appropriate constant. We give a criterion for positivity of the conjectural
constant, as well as some numerical evidence for our conjecture.

31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio