Convicted Boston Marathon bomber Dzhokar Tsarnaev is asking for a new trial.

Tsarnaev's lawyers filed an appeal on Monday, saying he didn't get a fair trial because of the trial's publicity.

Among the points his legal team argues is that the jurors were using social media during the trial and wouldn't have been able to avoid news about it. They're also taking issue with Tsarnaev's death sentence, claiming it may be unconstitutional.

Tsarnaev was given the death penalty back in June for carrying out the April 15th, 2013 bombings that left three people dead and injured over 200 others.

His brother Tamerlan also took part in the bombings and was killed in a shootout with police.  (Metro Networks Inc.)

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