  The astrophysical sources responsible for ultra high-energy cosmic rays
(UHECRs) continue to be one of the most intriguing mysteries in astrophysics.
We present a comprehensive search for correlations between high-energy
($\gtrapprox 1$ GeV) gamma-ray events from the Fermi Large Area Telescope (LAT)
and UHECRs ($\gtrapprox 60$ EeV) detected by the Telescope Array and the Pierre
Auger Observatory. We perform two separate searches. First, we conduct a
standard cross-correlation analysis between the arrival directions of 148
UHECRs and 360 gamma-ray sources in the Second Catalog of Hard Fermi-LAT
sources (2FHL). Second, we search for a possible correlation between UHECR
directions and unresolved Fermi-LAT gamma-ray emission. For the latter, we use
three different methods: a stacking technique with both a model-dependent and
model-independent background estimate, and a cross-correlation function
analysis. We also test for statistically significant excesses in gamma rays
from signal regions centered on Cen A and the Telescope Array hotspot. No
significant correlation is found in any of the analyses performed, except a
weak ($\lessapprox 2\sigma$) hint of signal with the correlation function
method on scales $\sim 1^\circ$. Upper limits on the flux of possible power-law
gamma-ray sources of UHECRs are derived.
