Transcendence of infinite sums of simple functions

摘要

In 1969, during a conference on number theory at Stony Brook, S. Chowla asked (see also [5]) if there was a rational-valued periodic function, not identically zero, with prime period p such that the series 00 f (n) n n=1 converges and vanishes. In 1973, Baker, Birch and Wirsing [3] answered this question negatively by proving the following theorem.