Ke$ha's Producer Dr. Luke Target of Twitter Death Threats

Ke$ha's music producer Dr. Luke is in serious danger, according to the LAPD, after some of the singer's fans went nuclear -- blaming Luke for her eating disorder.

LAPD's Threat Management Unit filed legal docs -- obtained by TMZ -- asking for a search warrant to hunt down the identity of people who are threatening Luke's life on Twitter.

The vengeful tweets started after TMZ ran a story that Ke$ha entered rehab for an eating disorder because Luke taunted her about her weight. Ke$ha's friend told us ... Luke told her she "looks like a f**king refrigerator."

In the search warrant docs, cops point out some of the tweets, including:

-- "You need to be worried because IMA slit your throat before January is over."
-- "You ugly fat ass bum bitch. Im gonna carve u like a pumpkin with a long sharp knife."
-- "Im gonna gut you like a fish then skin you and glue ur wrinkly raisin skin to a fridge!"
-- "I'm gonna slit your F**KIN throat open then gouge your eyeballs out."