Consequences of Apéry’s work on ζ(3)

Abstract

At the end of the 1970’s it seemed that my fate as a young beginning research mathematician was closely linked with work of Roger Apéry. My first acquaintance with his work was not through ζ(3), but through the diophantine equation x2 + D = pn in the unknown integers x, n, where D, p are given integers with p prime. This happened to be my thesis subject and the papers [A1,A2] turned out to be two very short but relevant papers on the subject. It was therefore a nice surprise for me to see Apéry ”live” during the Journées Arithmetiques in 1978 in Luminy. This surprise became excitement with Apéry’s announcement of his proof of ζ(3) ε/ Q and ended in utter confusion after hearing his famous lecture.