A Sharp Estimate for Divisors of Bernoulli Sums

Michel Weber

Let $S_n=\e_1+...+\e_n$, where $ \e_i $ are i.i.d. Bernoulli r.v.'s. Let $0\le r_d(n)<2d$ be the least residue of $n$ mod$(2d)$, ${\bar{r}}_d(n)=2d-r_d(n)$ and $\b(n,d)=\max ({1\ove…