Radiation from a quasi-periodically modulated electron beam is studied
using number theory. The quasi-periodic modulation consists of two di
fferent sinusoidal signals at frequencies omega(1) and omega(2). An el
ectron beam with such a modulation radiates at a third frequency, omeg
a(0). It is shown that the electron radiation is dominated by an inter
action among these three frequencies and the radiation frequency may b
e different from any integral multiple of either modulation frequency.