  (abridged) We present a statistical study of the low-mass X-ray binary (LMXB)
populations of three nearby, old elliptical galaxies: NGC 3379, NGC 4278, and
NGC 4697. With a cumulative ~1 Ms Chandra ACIS observing time, we detect 90-170
LMXBs within the D25 ellipse of each galaxy. Cross-correlating Chandra X-ray
sources and HST optical sources, we identify 75 globular cluster (GC) LMXBs and
112 field LMXBs. In the low luminosity range allowed by our deeper data (LX < 5
x 1037 erg s-1), we find a significant relative lack of GC-LMXBs, when compared
with field sources. Using the co-added sample from the three galaxies, we find
that the incompleteness-corrected X-ray luminosity functions (XLFs) of GC and
field LMXBs differ at ~4# significance at LX < 5 x 1037 erg s-1. As previously
reported, these XLFs are consistent at higher luminosities. Our observations
may indicate a potential predominance of GC-LMXBs with donors evolved beyond
the main sequence, when compared to current models, but their efficient
formation requires relatively high initial binary fractions in clusters. The
field LMXB XLF can be fitted with either a single power-law model plus a
localized excess at a luminosity of 5-6 x 1037 erg s-1, or a broken power-law
with a similar low-luminosity break. This XLF may be explained with
NS-red-giant LMXBs, contributing to ~15% of total LMXBs population at ~5x1037
erg s-1. The difference in the GC and field XLFs is consistent with different
origins and/or evolutionary paths between the two LMXB populations, although a
fraction of the field sources are likely to have originated in GCs.
