I could assume that Fritz David Carlson (1888–-1952) was at least his informal advisor, although Carlson was a Swedish mathematician. Note that he is not represented in the Mathematics Genealogy Project.
Selberg's first contribution to the Polya-Gelfond problem was very close in style to Carlson's famous theorem (see, for example, [P.J. Forrester and S.O. Warnaar, The importance of the Selberg integral, Trans. Amer. Math. Soc. 45 (2008) 489--534]