 Lacunary Fourier series

A Hadamard-lacunary Fourier series has nonzero frequencies supported on a positive sequence with the displayed gap ratio, possibly together with its negatives and finitely many extra modes. Such gaps strongly restrict additive frequency relations. They make moment estimates resemble those of independent random variables. For a ratio greater than three, the strongly lacunary polynomial L1-L2 bound follows directly by enumerating fourth-moment pairings.