Title: On the coefficients of symmetric power $L$-functions,
Abstract: We study the signs of the Fourier coefficients of a newform. Let $f$ be a
normalized newform of weight $k$ for $\Gamma_0(N)$. Let $a_f(n)$ be the $n$th
Fourier coefficient of $f$. For any fixed positive integer $m$, we study the
distribution of the signs of $\{a_f(p^m)\}_p$, where $p$ runs over all prime
numbers. We also find out the abscissas of absolute convergence of two
Dirichlet series with coefficients involving the Fourier coefficients of cusp
forms and the coefficients of symmetric power $L$-functions.