Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-linear additive twist of Fourier coefficients of $GL(3) \times
  GL(2)$ and $GL(3)$ Maass forms   Let $\lambda_{\pi}(m,n)$ be the Fourier coefficients of a Hecke-Maass cusp
form $\pi$ for $SL(3,\mathbb{Z})$ and $\lambda_{f}(n)$ be the Fourier
coefficients of Hecke-eigen form $f$ for $SL(2,\mathbb{Z})$. The aim of this
article is to get a non-trivial bound on the sum which is non-linear additive
twist of the coefficients $\lambda_{\pi}(m,n)$ and $\lambda_{f}(n)$. More
precisely, for any $0 < \beta < 1$ and $\epsilon>0$, we have
$$\sum_{n=1}^{\infty} \lambda_{\pi}(r,n) \, e\left(\alpha n^{\beta}\right)
V\left(\frac{n}{X}\right) \ll_{\pi,\epsilon} \alpha
\sqrt{\beta}r^{\frac{7}{6}}X^{\frac{3}{4}+\frac{9\beta}{28}+ \epsilon}.$$ and
$$\sum_{n=1}^{\infty} \lambda_{\pi}(r,n) \, \lambda_{f}(n) \, e\left(\alpha
n^{\beta}\right) V\left(\frac{n}{X}\right) \ll_{\pi, f,\epsilon} (\alpha
\beta)^{\frac{3}{2}} rX^{\frac{3}{4}+\frac{29\beta}{44}+\epsilon},$$ where
$V(x)$ is a smooth function supported in $[1,2]$ and satisfying $V^{(j)}(x)
\ll_{j} 1$.

31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio