Let $1<r<2$ be a real number. Let $4<p\le 6$. Consider the exponential sum estimate $$\int_0^{2\pi}\int_0^{N^{r-2}} \left|\sum_{n=1}^N e^{inx+in^2 y}\right|^p \, dy \, dx$$ Notice that the $y$ variable takes values in an interval of length much smaller than one. My question is, as $N\to \infty$, what is the sharp bound on the above exponential sum?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.