Irrational power series. III

Abstract

Several writers (see [1 ] for references) have shown that if f(y) satisfies various conditions, then F(x) is not a rational function of x, and some have shown that the circle x| = 1 is a line of essential singularities for F(x). I notice a very simple way of dealing with such questions. The method is really that of Hecke, but its possibilities have not been fully explored. I now prove the THEOREM. Let f(x) be Riemann integrable in 0? x< 1, and let I be any integer. Then as x?e2Ir ia along a radius from x =0,

Locations

• Proceedings of the American Mathematical Society - View - PDF