I could assume that <a href="http://en.wikipedia.org/wiki/Fritz_Carlson">Fritz David Carlson</a> (1888–-1952) was at least his informal advisor, although Carlson was a Swedish mathematician. Note that he is not represented in the <a href="http://genealogy.math.ndsu.nodak.edu/">Mathematics Genealogy Project</a>.

Selberg's first contribution to the Polya-Gelfond problem was very close in style to Carlson's famous theorem (see, for example, 
<a href="http://www.maths.uq.edu.au/~uqowarna/pubs/Selberg_review.pdf">[P.J. Forrester and S.O. Warnaar, The importance of the Selberg integral, *Trans. Amer. Math. Soc.* **45** (2008) 489--534]</a>