Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A further discussion on quasar-galaxy associations from gravitational
  lensing   Quasar-galaxy associations, if they result from the effect of gravitational
lensing by foreground galaxies, depend sensitively on the shape of the quasar
number counts. Two kinds of quasar number-magnitude relations are predicted to
produce quite different properties in quasar-galaxy associations: the counts of
Boyle, Shanks and Peterson (1988; BSP) provide both positive and ``negative"
associations between distant quasars and foreground galaxies, relating closely
with the knee ($B\approx19.15$) in these counts. However, Hawkins and V\'eron
(1993; HV) quasar data lead to only a positive magnitude-independent
quasar-galaxy association. The current observational evidence on quasar-galaxy
associations, either positive or null, is shown to be the natural result of
gravitational lensing if quasars follow the BSP number-magnitude relation. On
the other hand, the HV counts are unable to produce the reported associations
by the mechanism of gravitational lensing. It is emphasized that special
attention should be paid to the limiting magnitudes in the selected quasar
samples when one works on quasar-galaxy associations.

9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat