ARPACK is a collection of Fortran77 subroutines designed to solve large scale eigenvalue problems. ARPACK should be readily packaged by most Linux distributions. Don't forget to install a development version of the library.
Below is a short summary of instructions on how to compile and install ARPACK by hand (for the case you wish to do so).
After you downloaded the Fortran version of ARPACK and the patch, unzip the files you got. That will create a directory named ARPACK. If you need further instructions please read the README file or the instructions. We will explain here in a few steps what has to be done to be able to compile ARPACK.
ARmake.incmake lib in the current directory
      to build the standard library libarpack_$(PLAT).a
      
    Note: For compilation of ARPACK we emphasise
    adding the compiler flag -fPIC. This is a definite
    requirement if we are compiling deal.II with
    shared libraries (which is the default). If we had preferred to be
    compiling deal.II without shared libraries,
    that's ok too; in that case we would do exactly the same thing
    as described above, but this time omitting
    the -fPIC flag from the scheme.
    
    Try to run one of the examples and compare the output.
    How the output should look like is stated in the README
    that can be found in the EXAMPLES directory.
    
If that output you produced looks like it should you can proceed to compile deal.II with ARPACK.
Support for ARPACK will be enabled automatically if a system wide installation of ARPACK can be found. To use a self compiled version, specify
    -DARPACK_DIR=/path/to/arpack
      
      when invoking cmake.
    
    You can override the autodetection by manually setting
    -DDEAL_II_WITH_ARPACK=OFF|ON
      .