Quoting the fiction of the bible as historical fact is shameful and I am surprised given PBS generally being run by the scientific and intellectual ranks of Americans. It brings me great sadness to see such a good historical program tarnished with endless superstitious injections. The Roman Empire made no reference to Jesus when or near when Jesus was said to exist. The Bible is a work of fiction that draws endlessly on other older stories from Confusus to Sargon. Please don't present these fictional works intermixed with historical facts.Keep to accurate Science and History. Leave the rest for the endless religious programming available on the air waves.

After reading http://www.roman-empire.net/emperors/nero-index.html, Nero is cited as having persecuted them. Here is a quote from that webpage: "Nero, always a man desparate to be popular, therefore looked for scapegoats on whom the fire could be blamed. He found it in an obscure new religious sect, the Christians.
And so many Christians were arrested and thrown to the wild beasts in the circus, or they were crucified . Many of them were also burned to death at night, serving as 'lighting' in Nero's gardens, while Nero mingled among the watching crowds.
It is this brutal persecution which immortalized Nero as the first Antichrist in the eyes of the Christian church. (The second Antichrist being the reformist Luther by edict of the Catholic Church.)"

In part 3, Winds of Change, the information on Nero is largely misinformation from Tacitus who, according to his contemporaries, was one of the notorious liars of his day. Tacitus had an inexplicable hatred of Nero that tainted everything he wrote about the dead emperor. He is personally responsible for the poor and mostly untrue legacy of Nero: he wrote 'At the very time that Rome burned, he mounted his private stage and, reflecting present disasters in ancient calamities, sang about the destruction of Troy'. Tacitus also alleged Nero started and/or encouraged the fire. The fact is Nero was far from Rome [in Antium] when the fire began and rushed back to help fight the fire and arrange for care of the displaced. Tacitus also made the false claim that Nero persecuted christians. At that time there were very few christians in Rome and it's far more likely that Nero never actually saw a christian in his life. The new christian cult was only beginning during Nero's reign and its few followers were very far from Rome.
Nero was a good ruler in the eyes of the common people and his popularity among the lower classes remained even after his death. After the fire he imposed strict building laws for the reconstruction of the city, demanded wider streets, limited the height of buildings, and made laws that required the use of safer building materials. Nero also rebuilt large residential areas of Rome at his own expense.
During his reign the senate was treated respectfully and granted greater freedom. Sensible legislation was introduced to improve public order, reforms were enforced on the treasury and provincial governors were prohibited from extorting money. Nero himself followed in the steps of his predecessor Claudius in applying himself rigorously to his judicial duties.
He also considered liberal ideas, such as ending the killing of gladiators and condemned criminals in public spectacles.
[Partly condensed from http://www.roman-empire.net/emperors/nero-index.html]