Let $A(n_1,n_2,\dots,n_{m-1})$ be the normalized Fourier coefficients of a Maass cusp form on $\textrm{GL}(m)$. In this paper, we study the cancellation of $A (n_1,n_2,\dots,n_{m-1})$ over Beatty sequences.

Let $\tau(n)$ be the Ramanujan $\tau$-function. We prove that for any integer $N$ with $|N|\ge 2$ the diophantine equation $$\sum_{i=1}^{148000}\tau(n_i)=N$$ has a solution in positive integers $n_1, n_2,\ldots, n_{148000}$ satisfying the condition $$\max_{1\le i\le 148000}n_i\ll |N|^{2/11}e^{-c\log |N|/\log\log |N|},$$ for some absolute constant $c>0.$

In this note we show that for an arbitrary reductive Lie group and any admissible irreducible Banach representation the Mellin transforms of Whittaker functions extend to meromorphic functions. We locate the possible poles and show that they always lie along translates of walls of Weyl chambers.