Part 2: Automorphic Functions

I was introduced to this theme by I. M. Gelfand. In Vol. VI of the famous series “Generalized Functions”, which he was preparing together with I. O. Piatezky-Shapiro, he wanted to expose the Selberg theory for SL(2,R) with noncompact fundamental domain of finite volume. In this case the corresponding Laplacian has continuous spectrum and the authors needed tools to treat it. As a specialist in continuous spectrum I was invited to supply them with these tools. I was given two weeks to do it. So I worked hard and produced a text with the proof of completeness of the Eisenstein series. I. M. Gelfand found my exposition too sophisticated to be included into the monograph and the book was published without the treatment of noncompact case. My text was put aside and was finally published in [2-1] several years later. It was populized by S. Lang, who made a detailed exposition of it in his book SL(2,R)…