Weil's Riemann Hypothesis is a deep result that I don't fully understand, but it has understandable corollaries which interest me. For example:

(a) For any projective curve $X$ satisfying certain conditions, the number $N$ of points in $X$ with coordinates in $\mathrm{GF}(q)$ satisfies $|N-(q+1)|\leq\mathrm{const}\cdot\sqrt{q}$. (The deviation is $0$ when $X$ is a projective line.)

(b) For any nontrivial multiplicative character $\chi$ on $\mathrm{GF}(q)$ and any polynomial $f$ of degree $n$ satisfying certain conditions, we have 

$$\bigg|\sum_{x\in\mathrm{GF}(q)}\chi(f(x))\bigg|\leq(n-1)\sqrt{q}.$$

Questions:


Is there a reference (legible to an English-speaking non-expert in the field) which gives the rigorous statements of these corollaries? In particular, I would like conditions which one can verify without a background in algebraic geometry.
Are there other corollaries of Weil's Riemann Hypothesis which are also widely understandable? EDIT: I'm mostly interested in the Riemann Hypothesis, but I'm also happy to learn understandable consequences of the other Weil conjectures and related results.



Question: Unreachable IP on local subnet
Answer: I have the same problem today. Check the mac address of your Ubuntu machine and printer, they have a same mac address, so change your Ubuntu mac address to fix this problem.