It appears that no single mathematician at Oslo had that much influence on Selberg. There is a long translated interviewat http://www.ams.org/journals/bull/2008-45-04/S0273-0979-08-01223-8/. He defended his dissertation on October 22, 1943. The Germans closed the university on November 30. Given the kind of people with whom he was corresponding and the comparatively little time he actually spent at Oslo, it may be that the professors flipped a coin after his defense as to the order of signatures.
Well, this may be an injustice to someone we currently do not know about, but Selberg seems to have done everything himself.
There may be reason to think Carl Stormer Størmer (with an o umlaut) 1874–-1957) was the adviser. He was present at the defense and presented the paper to the Norwegian academy of Sciences. Evidently the expert asked to comment was elsewhere, Harald Bohr, (1887-–1951), brother of Niels.
