We report on a search for electronic recoil event rate modulation signatures in the XENON100 data accumulated over a period of 4 years, from January 2010 to January 2014. A profile likelihood method, which incorporates the stability of the XENON100 detector and the known electronic recoil background model, is used to quantify the significance of periodicity in the time distribution of events. There is a weak modulation signature at a period of $431^{+16}_{-14}$ days in the low energy region of $(2.0-5.8)$ keV in the single scatter event sample, with a global significance of $1.9,sigma$, however no other more significant modulation is observed. The expected annual modulation of a dark matter signal is not compatible with this result. Single scatter events in the low energy region are thus used to exclude the DAMA/LIBRA annual modulation as being due to dark matter electron interactions via axial vector coupling at $5.7,sigma$.
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