A movie review of “Me and Earl and the Dying Girl”: This sweet and smart comedy follows a couple of movie-mad teenagers who befriend a classmate stricken with leukemia. Rating: 3.5 stars out of 4.

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How many movie references can you squeeze into one sweet and funny film?

“Me and Earl and the Dying Girl” — the big winner at the 2015 Sundance Film Festival — tests the limits with a smart script built around a couple of movie-mad teenagers who can’t stop making low-budget imitations of “Mean Streets,” “Citizen Kane,” “Apocalypse Now” and other classics.

The three kids named in the title are high-school survivors. Greg (Thomas Mann) gets by mostly by making himself appear to be invisible. His best friend, Earl (RJ Cyler), helps him make miniature movies. Rachel (Olivia Cooke) is a classmate who has just been told she has leukemia.

Movie Review ★★★½  

‘Me and Earl and the Dying Girl,’ with Thomas Mann, Olivia Cooke, RJ Cyler, Molly Shannon, Nick Offerman, Connie Britton. Directed by Alfonso Gomez-Rejon, from a screenplay by Jesse Andrews. 104 minutes. Rated PG-13 for language. Several theaters.

Greg’s mother (Connie Britton) insists that Greg befriend her. Awkward at first, wary that their relationship is based on pity, the three form a bond that’s mostly drawn from Greg’s deadpan stand-up style. Mann is simply perfect for the role, and Cooke and Cyler bring a weight to their characters that lends a necessary balance to the movie’s tone.

Directed by Alfonso Gomez-Rejon, who worked as a second-unit director on the kinds of movies that Greg and Earl imitate, “Me and Earl” wholeheartedly embraces their Scorsese/Coppola fantasies, all but inviting the audience to share their obsession. So does the script by Jesse Andrews, delightfully adapted from Andrews’ own novel.