I’ve read before that although the Romans kept meticulous records of crucifixions, there is no surviving record of a Jewish radical from Nazareth being crucified in the claimed time period. I don’t have references handy, but I can dig some up if anyone’s interested. Christian scholars, when presented with this lack of evidence, have sometimes argued the lack of a record is due to the fact that Jesus was crucified by Jews, not by Romans. However, this Christian scholar actually argues that Jesus wasn’t crucified at all:
The legend of his execution is based on the traditions of the Christian church and artistic illustrations rather than antique texts, according to theologian Gunnar Samuelsson.
He claims the Bible has been misinterpreted as there are no explicit references the use of nails or to crucifixion – only that Jesus bore a “staurus” towards Calvary which is not necessarily a cross but can also mean a “pole”. […]
The ancient Greek, Latin and Hebrew literature from Homer to the first century AD describe an arsenal of suspension punishments but none mention “crosses” or “crucifixion.”
Mr Samuelsson, of Gothenburg University, said: “Consequently, the contemporary understanding of crucifixion as a punishment is severely challenged.
“And what’s even more challenging is the same can be concluded about the accounts of the crucifixion of Jesus. The New Testament doesn’t say as much as we’d like to believe.”
(via Dangerous Meme)
However, I would expect the Romans would have kept records of all executions, crucifixions or not, though I suppose the “he was executed by Jews” caveat would still apply.
Samuelsson also claims “That a man named Jesus existed in that part of the world and in that time is well-documented. He left a rather good foot-print in the literature of the time.” My understanding is that there are no surviving contemporary accounts of Jesus, but I could be wrong.
(I still subscribe the “composite character” theory of Jesus – he was based on several historical Jewish radicals, not a historical single person, and later sexed up with Pagan mythology to make Christianity more palatable)