All Questions

There is a basic question which puzzles me for a while, and maybe look naive for some experts here. The question is the following: Let $f(z)=\sum_{n\ge 1} a_f(n) n^{k/2-1/4}e(nz)\in S_{k+1/2}(4N)$ be ...

For $m,n\in \mathbb{N}$, denote the Kloosterman sum $$S(m,n;c)=\sum_{a\bmod c}e\left( \frac{ma+n \overline{a}}{c}\right),$$where $\overline{a}$ denotes the multiplicative inverse of $a\bmod c$. Does ...

I hope someone can tell me something about the error term in the formula calculating the oscillatory integral like $\int_a^b g(x)e(f(x))d x$. Specially, the exact formula on page 114 of M. Huxley's ...