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That's the problem with these lists - you say it is to be of the “greatest” crime writers but then ask me for my “favourites”, and the two may not be at all the same, even in my own mind. I enjoy Jilly Cooper as much as Anthony Powell, but I know the one to be important and the other probably not so.
Writers whose work has helped me as a crime writer include Dickens for Bleak House, R. L. Stevenson for Jekyll and Hyde, James Hogg for Confessions of a Justified Sinner, Muriel Spark (below) for The Driver's Seat and William McIlvanney for Laidlaw, but I wouldn't class any one of them as a crime writer.
I'd probably say the five greatest crime writers (in terms of popularity, ingenuity, influence) were Conan Doyle, Christie, Chandler, McBain and Highsmith. But then I'd be missing out Simenon, Thomas Harris, Patricia Cornwell, etc.
My five personal favourites (as of this minute) would be Chandler, James Ellroy, Ruth Rendell, George Pelecanos and Reginald Hill. But ask me again tomorrow and I might opt for Michael Connelly, Denise Mina, David Peace, Elmore Leonard and Josephine Tey. Oh, and how could I forget the likes of James Lee Burke, Hammett, Sayers, John Creasey, Lawrence Block, Minette Walters, P.D. James, Val McDermid, Colin Bateman, Leo Malet, Fred Vargas, Leonardo Sciascia (and Umberto Eco for Name of the Rose)? It's like going on Desert Island Discs. I always regretted leaving out Silver Machine by Hawkwind...
Ian Rankin's latest novel is Exit Music

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Some of these folk I've never heard of. Thanks, Ian. Off I go to plunder for books.
Sal Towse, San Francisco, USA
Thanks, Ian for listing Leo Malet even if it's on your tomorrow's list. Malet, little known outside France and a major force in the 50's 60's crime genre inspired also a whole series of illustrated books...graphic novels based on his detective Nestor Burma's investigations in Paris. To me he ranks with Simenon and please no one shoot me for that.
Cara Black, San francisco, ca usa