After 14 years and multiple spinoffs, chances are you’ve seen an episode of the TV franchise “CSI” at least once in your life. Perhaps you watch “Bones” on a semi-regular basis. Or maybe you prefer “Criminal Minds,” or “Castle,” or “Burn Notice.”

But have you read them?

Browse Amazon’s digital shelves and you’ll find original books inspired by popular television series like “Revenge,” “24,” “Veronica Mars,” “Supernatural,” “Grimm” and more.

These aren’t novelizations of existing episodes. They’re new works, written by established authors, that deepen the characters’ backstories, add to the program’s overarching universe and keep viewers hooked during those long hiatus months. And while some might scoff without ever having read one, these tie-ins can be every bit as gripping as any other work of genre fiction.

With that in mind, I urge fans of “The Killing” to pick up a copy of Karen Dionne’s recently released novel “The Killing: Uncommon Denominator.” More than just a solid prequel to the series, it’s an atmospheric, impressively-hardboiled thriller in its own right.

Based on a Danish police drama called “Forbrydelsen” (or “The Crime”), the Americanized version premiered on AMC a few years ago and just wrapped up its fourth, and supposedly final, season on Netflix.

Since the show’s two main characters, Linden and Holder, are introduced to each other in the first season, one of the pleasures of the book is seeing how close they repeatedly come to crossing paths. There’s a witty “Rosencrantz and Guildenstern” aspect to the tale, a playful gamesmanship to the way that Dionne continually toys with what we already know about the series and its characters.

The book can easily be enjoyed without having seen an episode, but for longtime viewers it’s a far richer experience. There’s a chilling moment late in the novel where Linden, while searching an eerily deserted house, hears a child crying softly behind a closet door. For a split-second she freezes, remembering another child who hid behind a similar door in the past, a child whose trauma formed a major subplot in the show’s disturbing third season. An earlier sequence finds Linden out of her jurisdiction at an Indian casino, where she receives a bitter cold-shoulder from the security staff and management. Astute viewers know that the casino is destined to become an important location during the Rosie Larsen murder case from the first season.

Fans of the series are in for some wonderful shivers of recognition throughout the story.

Set in Seattle, but shot in Canada, “The Killing” was one of the frostiest shows in recent memory, and Dionne expertly captures its frigid, rain-soaked landscape with a cinematographer’s eye for detail. This is a bleak, cold book, filled with gray skies, torrential downpours and cops huddled inside cars to keep warm. In one particularly evocative scene, you can practically smell the icy breath of the junkies gathered around a trash-fire beneath an overpass, with undercover officer Holder secretly among them.

Dionne’s prose style, especially during the first few chapters, is clipped and terse, cutting directly to the point. There’s a “just-the-facts-ma’am” vibe to her writing, a lean Joe Friday-esque directness that works nicely within the world of the show. It’s punchy stuff.

Like the TV series, the book is structured in 24-hour blocks of time, with each section marking another day of the investigation. What’s unique is the way that Dionne alternates between her three main characters: Linden, Holder and a new Detective named John Goddard. This is due to the fact that, in order to maintain continuity with the program, Linden and Holder can’t be allowed to meet in person. Dionne carefully plots the novel to keep them apart, using Goddard as a go-between when necessary. It’s a technique that works well, thanks in large part to Goddard himself.

A warmer, more easily relatable character than either Linden or Holder, Goddard is a welcome addition to the series. It’s interesting to see the way that he views the other two detectives, particularly Linden whom he partners with when their individual investigations merge. We sense that although he respects her skills as a cop, he doesn’t entirely trust her judgment in other areas. Considering how emotionally damaged she is, that’s probably wise.

Holder takes a slight backseat role, but when he’s the focus of attention it’s easy to imagine Joel Kinnaman’s twitchy performance. There’s a quiet sadness to Holder that Dionne clearly understands, a lost quality that makes us root for him, whether onscreen or on the page.

The book’s version of Linden is every bit as flawed as the one portrayed so hauntingly by actress Mireille Enos. From her constant chain smoking, to her awful mothering, to her control-freak need to always drive, Dionne paints Linden as a walking-wounded survivor of the foster care system. There’s a heartbreaking sequence in the novel where Linden returns to the lonely child placement agency that she was once a part of. Entering the building, she’s both fearful and curious, a tightly-wound cop coming face-to-face with her past. Dionne allows us to glimpse that inner conflict and the result is quite moving.

As for the actual murder case that propels the story, it’s decent, but not amazing. Unlike the grisly, sexualized murder of Rosie Larsen in the first two seasons, or the creepy serial killings in the third, the deaths in the book lack a sense of palpable horror. Perhaps that’s because the victims are middle-aged men, killed for financial reasons, not vulnerable teens and street kids being stalked by psychos. I must admit, I missed the nightmarish quality of those earlier crimes.

Another area where the show trumps the book is in its use of well-drawn supporting roles. There were times when the novel felt slightly under-populated. The TV series spent a great deal of time with important side-characters, like the grief-stricken Larsen family, Darren Richmond and his campaign staff, Bullet and her fellow runaways and especially death row inmate Ray Seward and the prison staff. They helped flesh-out the narrative, adding layers of depth that the novel sometimes lacks.

Overall though, “The Killing: Uncommon Denominator” (admittedly not the greatest title in the world), is an engrossing crime novel and an excellent prequel to the television series. I suspect it’ll please fans who aren’t ready to say goodbye quite yet to Linden and Holder. Speaking as one of them, I hope that Dionne writes another book in the series… and another one after that.

May the killing continue.