Bounds for exponential sums with random multiplicative coefficients

Seth Hardy

For $f$ a Rademacher or Steinhaus random multiplicative function, we prove that $$ \max_{θ\in [0,1]} \frac{1}{\sqrt{N}} \Bigl| \sum_{n \leq N} f(n) \mathrm{e} (n θ) \Bigr| \gg \sqr…