Hans Maass

Hans Maass (Hans Maaß; June 17, 1911, in Hamburg – April 15, 1992) was a German mathematician who introduced Maass wave forms and Koecher–Maass series   and Maass–Selberg relations and who proved most of the Saito–Kurokawa conjecture. Maass was a student of Erich Hecke.

Maaß was primarily concerned with the theory of modular forms, being influenced in particular by Carl Ludwig Siegel (according to Maaß in his inaugural address for admission to the Heidelberg Academy, he met him in the early 1950s), whose Gesammelte Werke he also co-edited with K. S. Chandrasekharan, in addition to Hecke and Hans Petersson - Hecke's assistant at the time, who suggested the topic of his dissertation. He became known for his introduction of non-analytic automorphic forms in the 1940s (Maaß waveforms). Instead of satisfying Laplace's equation (as analytic functions do), they are eigenfunctions of the invariant Laplace operator; Maaß therefore called them waveforms. Internationally, these forms are known by his name. The motivation for the introduction came in part from Maaß's interest in connections of the theory of modular forms to number theory. Maaß was also concerned with automorphic functions in several variables, Siegel modular functions, and associated zeta functions.

Publications

 * Maass, H. (1949), "Automorphe Funktionen von mehreren Veranderlichen und Dirichletsche Reihen", Abh. Math. Sem. U. Hamburg 16:72–100.
 * Maass, H. (1949), "Automorphe Funktionen von mehreren Veranderlichen und Dirichletsche Reihen", Abh. Math. Sem. U. Hamburg 16:72–100.