(Reuters) - Former Penn State football coach Jerry Sandusky appealed his child sex abuse convictions on Thursday, with his lawyers arguing they lacked time to prepare for the high-profile case.

Sandusky's attorneys also asked that the convictions be tossed out or a new trial be held because prosecutors lacked evidence to convict him and statutes of limitations had run out.

Sandusky, 68, was convicted in June on 45 counts of sexually abusing 10 boys in a case that stunned Pennsylvania State University and the public. He was sentenced this month to 30 to 60 years in prison.

His attorneys, Joe Amendola and Karl Rominger, had said they would appeal because Sandusky's constitutional rights to due process were violated.

The 31-page appeal, filed in Pennsylvania's Centre County Court, said defense lawyers did not have enough time to go through documents, compact discs, hard drives, photos and other evidence and to question potential witnesses before trial.

Judge John Cleland erred in denying motions for continuance. Subpoenas were still being answered "up until and including trial," the appeal said.

Statutes of limitations had run out for eight of the 10 victims, Sandusky's attorneys argued. Prosecutors failed to show enough evidence to convict Sandusky and the charges were not specific enough, they said.

The appeal argued that the defense lacked time to present psychiatric testimony and hire a jury consultant.

It also seeks to modify Sandusky's sentence, saying the mandatory terms should have been concurrent instead of mandatory.