We super-resolve the seeing-limited Subaru Hyper Suprime-Cam (HSC) images for
32,187 galaxies at z~2-5 in three techniques, namely, the classical
Richardson-Lucy (RL) point spread function (PSF) deconvolution, sparse
modeling, and generative adversarial networks to investigate the environmental
dependence of galaxy mergers. These three techniques generate overall similar
high spatial resolution images but with some slight differences in galaxy
structures, for example, more residual noises are seen in the classical RL PSF
deconvolution. To alleviate disadvantages of each technique, we create combined
images by averaging over the three types of super-resolution images, which
result in galaxy sub-structures resembling those seen in the Hubble Space
Telescope images. Using the combined super-resolution images, we measure the
relative galaxy major merger fraction corrected for the chance projection
effect, f_merg, for galaxies in the ~300 deg^2-area data of the HSC Strategic
Survey Program and the CFHT Large Area U-band Survey. Our f_merg measurements
at z~3 validate previous findings showing that f_merg is higher in regions with
a higher galaxy overdensity delta at z~2-3. Thanks to the large galaxy sample,
we identify a nearly linear increase in f_merg with increasing delta at z~4-5,
providing the highest-z observational evidence that galaxy mergers are related
to delta. In addition to our f_merg measurements, we find that the galaxy
merger fractions in the literature also broadly align with the linear
f_merg-delta relation across a wide redshift range of z~2-5. This alignment
suggests that the linear f_merg-delta relation can serve as a valuable tool for
quantitatively estimating the contributions of galaxy mergers to various
environmental dependences. This super-resolution analysis can be readily
applied to datasets from wide field-of-view space telescopes such as Euclid and
Roman.Comment: 29 pages, 13 figures, 6 tables. Submitted to PASJ. Comments welcom