On Fabry's Gap Theorem

Jan-Christoph Puchta

Address. Mathematisches Institut der Universitaet Freiburg, Eckerstrasse 1, 79111 Freiburg, Germany

E-mail: jcp@arcade.mathematik.uni-freiburg.de

Abstract. By combining Tur\'an's proof of Fabry's gap theorem with a gap theorem of P.
Sz\"usz we obtain a gap theorem which is more general then both these theorems.

AMSclassification. 30A10, 30B10, 11N30.

Keywords. Gap theorems, lacunary series, power sum method.