The Bohnenblust-Hille cycle of ideas from a modern point of view

Abstract

In 1931 H.F. Bohnenblust and E. Hille published a very important paper in which not only did they solve a long standing problem on convergence of Dirichlet series, but also gave a~general version of a celebrated inequality of Littlewood. Although it is full of extremely valuable mathematical ideas, the paper has been overlooked for a~long time and even today we feel that it does not get the credit it deserves. This may be caused by the not always accessible style that makes that the ideas are sometimes hidden. It is our intention to try to study the paper from a~modern point of view and to bring to light the valuable aspects we believe it has.