Trying to recall a novel from the early 2000s. A murder has been committed using a medical device based on a matter transmitter - normally used to "beam" infected organs and cancers from the body, it was used to send several people to the same point in space, with obviously messy and fatal results. The main protagonist is repeatedly killed during the investigation, and keeps coming back in a duplicate form, and has done so during other investigations. I keep thinking there's a number like "57" in the title.
This sounds like Version 43, a 2010 novel by Philip Palmer, the third book in his Debatable Space Universe series. The second book in the series, Red Claw (or Zone in the German edition), was the subject of this question. Here is a review from io9.gizmodo.com (emphasis added):
Far-future Earth is a peaceful place, with little crime and few anti-social personalities. That's because whenever someone commits a serious offense, they're offered a shot at a new life on the distant planet of Belladonna. Of course, you have to go by quantum teleportation, and there's a only fifty-fifty chance of surviving the trip, which means the planet is pretty much a madhouse. Corruption is endemic and law-breaking a way of life. But some things are beyond the pale, and so the discovery of a particularly horrific crime scene demands the attention of a Galactic Cop. And so arrives the same cyborg—now Version 43—who, a hundred years before, busted up all the gangs and straightened out the city. This time, he's going to make it stick.
Version 43 is a pulpy space-noir, so the dialogue is the best part. Everyone in Belladonna seems to have a smart mouth. The language is salty; more than once, our cybernetic hero is called "a cold, evil, fucking machine." One witness asks him whether there are "any other bits of my life you'd like to filthily dabble in." There is much cracking wise.
Against the background of all this colorful slang is Version 43's distinctly limited range of expression. Here he is, psyching himself up for a post-heist orgy: "My detailed forward planning was paying off; I designed my current body to be a fully functional replica of a human being—outwardly at least—able to participate fully in all social and sexual contexts." Here, by contrast, is gangster Billy Grogan on the same event: "Right lads and ladies, let's hit the whorehouse." Version 43 is robotically pedantic, which means even his friends say he's kind of a wanker.
But there's a reason for his awkwardness. Version 43 is reborn into a new body every time he's killed, but all his emotional memories are erased. That leaves his ability to express himself rather limited, which has real consequences for the plot. Every time, the cyborg wakes up and thinks: "The previous Version was defective. This time, I'm going to clean up this planet, for once and for all." It's the only goal he can articulate, so he fixates, and then he pursues some harebrained scheme until he's killed yet again. The plan never works. As a plot device, this can get pretty frustrating—every time the character picks up some forward momentum, he's blown up and reverts to an insufferable cyborg wanker.
The world building is also solid. Palmer spends little time on description, and I couldn't tell you whether Lawless City looks more like Tokyo or New York or Rio. Instead, he does a great slow reveal of the planet's social hierarchy. Version 43 spends much of his time with the gangs, so we learn that each one has evolved to fit some niche in the criminal ecosystem. The Golgothian Irish handle the robberies and run some lovely bars, while the sleek Hari Gilles heads up an empire of Houses of Pain and boasts a crack squad of ninjas. These criminals are some of the most charming, entertaining characters in the book.
And then, there are the Hive Rats, the subject of an amusing (but confusing) side plot. At first glance, they're an underdeveloped race of sand-dwelling rodents. As it turns out, they're really controlled by a collective consciousness with several individual personalities, including the megalomaniacal First (determined to exterminate the human race) and the foul-mouthed Sixth (formerly a human admiral). Palmer creates distinct voices for each, using strictly their set-off dialogue, and the effect provides some of the book's funniest moments.
Overall, this is a self-consciously alt kind of book. The structure is playful and the dialogue ironic. Despite the noir vibe, this isn't a truly dark book. There's lots of shootouts and explosions. There's a borderline deus-ex-machina ending to die everything up. If you don't like that kind of thing, this isn't your book; if you do, you'll enjoy this inventive, pulpy romp.