We report on the detection of excess hard X-ray emission from the TeV BL Lac object Mrk 421 during the historical low-flux state of the source in January 2013 . NuSTAR observations were conducted four times between MJD 56294 and MJD 56312 with a total exposure of 80.9 ksec .
The source flux in the 3 - 40 keV range was nearly constant except for MJD 56307 , when the average flux level increased by a factor of three .
Throughout the exposure , the X-ray spectra of Mrk 421 were well represented by a steep power-law model with a photon index of \Gamma \simeq 3.1 , although a significant excess was noted above 20 keV in the MJD 56302 data when the source was in its faintest state .
Moreover , Mrk 421 was detected at more than the 4 \sigma level in the 40 - 79 keV count maps for both MJD 56307 and MJD 56302 but not during the remaining two observations .
The detected excess hard X-ray emissions connect smoothly with the extrapolation of the high-energy \gamma -ray continuum of the blazar constrained by Fermi -LAT during the source quiescence .
These findings indicate that , while the overall X-ray spectrum of Mrk 421 is dominated by the highest-energy tail of the synchrotron continuum , the variable excess hard X-ray emission above 20 keV ( on the timescale of a week ) is related to the inverse Compton emission component .
We discuss the resulting constraints on the variability and spectral properties of the low-energy segment of the electron energy distribution in the source .