Matruchus: He really managed to bring about a very funny russian accent in the Star Trek world. I think he was actually better then original Chekov (Walter Koenig) from original Star Trek.
Indeed. What people often forget is that when you're bilingual, it's often difficult to "fake" the accent of one language when speaking in the other. Anton was perfectly bilingual, speaking both Russian and English fluently, so his "fake" Russian accent probably required a lot more effort than for most people.
Hopefully the production team of Star Trek Beyond will be able to sneak a quick tribute to him in the film's opening or end credits, although I suspect the final cut is already complete.