Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strong orthogonality between the Mobius function and nonlinear
  exponential functions in short intervals   Let $\mu(n)$ be the M\"obius function, $e(z) = \exp(2\pi iz)$, $x$ real and
$2\leq y \leq x$. This paper proves two sequences $(\mu(n))$ and $(e(n^k
\alpha))$ are strongly orthogonal in short intervals. That is, if $k \geq 3$
being fixed and $y\geq x^{1-1/4+\varepsilon}$, then for any $A>0$, we have \[
  \sum_{x< n \leq x+y} \mu(n) e\left(n^k \alpha \right) \ll y(\log y)^{-A} \]
uniformly for $\alpha \in \mathbb{R}$.

27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci