Harris, Murray J. "Chapter Twelve: References to Jesus in Early Classical Authors." in Wenham, David (editor), The Jesus Tradition Outside the Gospels. Sheffield: JSOT Press, 1984, 343-368.
Harris uses the term, "early classical authors" in a way unfamiliar to me, and possibly to others. He is speaking of late antiquity, during the "silver Latin" period of the Roman empire. The four authors he deals with are Tacitus, Suetonius, the younger Pliny, and Thallus (Wenham [editor] 1984, 343).
Thallus was a Christian author, preserved in fragments. He does describe the darkness which coincided with the crucifixion (Wenham [editor] 1984, 343). Thallus is commented on by Julius Africanus, by Josephus, and by Eusebius.
Pliny the Younter (ca. 61-112 AD) served as a legate to Bithynia beginning in 110. Letters 96 and 97 of book 10 of his formal letters deal with the problem of Christianity (Wenham [editor] 1984, 345). His description of Christian meetings and ethics shows the Christians believed in Jesus as God and would assemble regularly for worship, prayer, and to sing (Wenham [editor] 1984, 346).
Tacitus (ca. 56-117 or after), in his Annals and Histories, provides a good deal of information about past events of the first century. In his description of the great fires of Rome (64 AD), he describes Nero as shifting blame for the fire from himself to Christians (Wenham [editor] 1984, 348). This may well have simply been an excuse to persecute Christians, rather than any suspicion that the Christians were arsonists. Tacitus does identify the Christians as followers of Jesus, executed under the command of Pilate (Wenham [editor] 1984, 349). Tacitus seems adequately certain of his facts, which he includes in accounts normally accepted as well researched. What is especially compelling to Harris is that the sources used by Tacitus appear hostile to Christians, yet they catalog events affirmed by friendly sources as well (Wenham [editor] 1984, 351).
Suetonius, ca 69-130 AD, was a prolific author working with a broad range of interests (Wenham [editor] 1984, 353). In book five of Lives, he describes Claudius' expulsion of Jews from Rome due to their involvement in riots regarding "Christ." Harris takes this to be a clear reference to conflicts between Jews and Christians (Wenham [editor] 1984, 354). Suetonius seems to refer to this as a title, not a proper name of an individual. He does seem to assume that Christ was in Rome and involved in the riots, but Harris considers this a reasonable misunderstanding (Wenham [editor] 1984, 355).
Harris concludes that the few details provided are significant corroboration of the time, means of execution, and subsequent controversy about Jesus (Wenham [editor] 1984, 357). Christianity may have received little attention because it was considered a religion to be ignored and scorned (Wenham [editor] 1984, 358). For this reason, historians only mentioned it if it seemed compelling. Harris concludes that the mention of Christianity in these circumstances is of great value.