In start Arena ,there are a quest whit the Gray Prince,

i go there ,kill all in it ,and in the end is a man, i kill him to, but then ,how do i finish the quest?

i cant find anything, and when i go back to arena, The Gray Prince said, i still dont find the proof of his birth, or something like that.

There should be a journal, in the place where you fought Lord Lovidicus.

A journal? have it a name?

but thanks, i will go again later.

Oh man I had that happen once. Walk ALL the way back (I wanted some scenery so didn't fast travel), talk to Princey, find out I forgot the journal. Then I just fast traveled back and forth.

Annoying when I get all absent minded and forget something in a game, especially on an RPG with big distances to cross.

Yes, but im not sure i forgot it, is it : Sir Amiel′s Journal ,the name on it, then i have it on my inventory?

The journal is on a table in the same room where you fought Lord Lovidicus. Sir Amiel's journal is for Knights.
The correct journal will tell the story about The Grey Princes fathers love of Orcish maids.

Yes. Oddly enough, it's called "Journal of the Lord Lovidicus."