I remember reading somewhere that there is a (probably a family of) quick false proof of the Riemann hypothesis that starts by using complex logarithms in a bad way, then does some elementary calculations and out pops the result. A perusal of the General Mathematics section of the arXiv also shows an abundance of presumably false proofs of the same. These tend to be somewhat... unclear and I'd prefer avoiding to look at them in any detail.
Question: Can anyone describe a quick false proof of the Riemann hypothesis?
Preferably I'd like one that has a very clear false step that misuses complex logarithms or $n$-th roots or some such gadget in an identifiable way. This is both because of my curiosity, and because I figure I could use it as an exercise problem for undergrads (if I ever end up teaching a course on complex analysis) to explain why they should be careful about taking logarithms.