LOFAR low-band antenna observations of the 3C295 and Bootes fields:
  source counts and ultra-steep spectrum sources
  We present LOFAR Low Band observations of the Bootes and 3C295 fields. Our
images made at 34, 46, and 62 MHz reach noise levels of 12, 8, and 5 mJy
beam$^{-1}$, making them the deepest images ever obtained in this frequency
range. In total, we detect between 300 and 400 sources in each of these images,
covering an area of 17 to 52 deg$^{2}$. From the observations we derive
Euclidean-normalized differential source counts. The 62 MHz source counts agree
with previous GMRT 153 MHz and VLA 74 MHz differential source counts, scaling
with a spectral index of $-0.7$. We find that a spectral index scaling of
$-0.5$ is required to match up the LOFAR 34 MHz source counts. This result is
also in agreement with source counts from the 38 MHz 8C survey, indicating that
the average spectral index of radio sources flattens towards lower frequencies.
We also find evidence for spectral flattening using the individual flux
measurements of sources between 34 and 1400 MHz and by calculating the spectral
index averaged over the source population. To select ultra-steep spectrum
($\alpha < -1.1$) radio sources, that could be associated with massive high
redshift radio galaxies, we compute spectral indices between 62 MHz, 153 MHz
and 1.4 GHz for sources in the Bo\"otes field. We cross-correlate these radio
sources with optical and infrared catalogues and fit the spectral energy
distribution to obtain photometric redshifts. We find that most of these
ultra-steep spectrum sources are located in the $ 0.7 \lesssim z \lesssim 2.5$
range.
