On Ingham's Summation Method

Abstract

Ingham (2) has defined the following summation method. A series ∑ an will be called summable (I) to s ifwhere as usual [x] is the greatest integer ⩽ x. (An equivalent method was described somewhat earlier by Wintner (7), who called it “an Eratosthenian method“; however, the notation (I) and the name “Ingham summability” introduced by Hardy (1) seem to have become usual.)