I heard from an expert that many L-functions (in number field) that satisfy (A) Euler product, (B) functional Equation, (C) Ramanujan-Petersson conjecture/theorem will most likely satisfy (D) RH. Thus any proof for RH should be universal, meaning that if you prove RH for an L-function, you are essentially able to prove RH for almost all other L-functions. This is why, for a probable proof of RH, one must seriously introduce all these three essential ingredients (A), (B), (C).
For Riemann zeta function $\zeta(s)$: $$\zeta(s)=\sum_{n=1}^{\infty}\frac{1}{n^s}\quad \Re(s)>1\tag{1}$$ The Euler product is:
$$\zeta(s)=\prod_{p\ \text{prime}}^{\infty}\frac{1}{1-p^{-s}}\quad \Re(s)>1\tag{2}$$
The functional equation is: $$\pi^{-s/2}\Gamma(s/2)\zeta(s)=\pi^{-(1-s)/2}\Gamma((1-s)/2)\zeta(1-s)\tag{3}$$
question 1 What does Ramanujan-Petersson conjecture specifically mean $\zeta(s)$ function?