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Attorneys for Boston Marathon bomber Dzhokhar Tsarnaev appealed his conviction and death sentence on Monday, arguing that publicity made it impossible for him to get a fair trial in the city and that capital punishment is unconstitutional.

In court papers, defense lawyer William Fick cited a recent dissent by U.S. Supreme Court Justice Stephen Breyer in which he said that he believes the death penalty "now likely constitutes a legally prohibited 'cruel and unusual punishment.'"

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However, the majority opinion in that very same case opened with the declaration that "capital punishment is constitutional."

Tsarnaev was sentenced to death in June for helping his older brother carry out the April 15, 2013, blasts that killed three people and injured and maimed more than 200 others.

The appeal claims that "continuous and unrelenting publicity" about the bombings, the defendant and his family, and wrenching survivor stories prevented him from getting an impartial hearing. It notes that Boston announced a new holiday marking the bombings while jurors were deliberating Tsarnaev's guilt.

As users of social media, the jurors would have found it impossible to avoid coverage, the appeal argues.

"Put simply, prejudicial media coverage, events, and environment saturated greater Boston, including the social networks of actual trial jurors, and made it an improper venue for the trial of this case," the court papers say.

The defense repeatedly asked for a change of venue before the trial began, but the requests were rejected by the judge.