Hans Petersson

Hans Petersson. Hans Petersson was a German mathematician who made fundamental contributions to the theory of modular forms and automorphic forms. A student of the renowned analyst Erich Hecke, he spent most of his career as a professor at the University of Münster. Petersson is best known for introducing the Petersson inner product, a crucial tool in modern number theory and harmonic analysis.

Biography

Hans Petersson was born in Breslau, then part of the German Empire. He began his university studies at the University of Breslau before transferring to the University of Hamburg, where he completed his doctorate in 1925 under the supervision of Erich Hecke. After his habilitation in 1928, he worked as a Privatdozent at University of Hamburg, collaborating closely with Carl Ludwig Siegel and Emil Artin. In 1935, he was appointed to a professorship at the University of Greifswald, and in 1940 he moved to a chair at the University of Münster, where he remained for the rest of his career, rebuilding the mathematical institute after World War II. Among his notable doctoral students were Martin Kneser and Hel Braun.

Mathematical work

Petersson's most celebrated contribution is the invention of the Petersson inner product, a Hermitian inner product defined on spaces of cusp forms. This construct provided a powerful Hilbert space structure, allowing for the application of spectral theory and leading to profound results on Hecke operators, including the proof of their simultaneous diagonalizability. His work, deeply rooted in the traditions established by Erich Hecke and Henri Poincaré, significantly advanced the analytic theory of modular forms. Petersson also made important studies on Poincaré series, Eisenstein series, and the Riemann-Roch theorem as applied to automorphic functions, influencing later developments in the Langlands program.

Selected publications

Throughout his career, Petersson authored numerous influential papers and monographs. A seminal early work is his 1930 paper "Über die Entwicklungskoeffizienten der automorphen Formen" in Acta Mathematica. His extensive research on modular forms was later synthesized in the comprehensive book "Modulformen und quadratische Formen," published by Springer-Verlag in 1982. Other significant works include studies on analytic continuation of Dirichlet series associated to modular forms and collaborations with Max Koecher on Jordan algebras and their relation to automorphic forms.

Awards and honors

For his foundational work, Petersson was elected a corresponding member of the Akademie der Wissenschaften zu Göttingen. He was also honored with a dedicated issue of the journal Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg on the occasion of his 60th birthday. His legacy is permanently enshrined in mathematical terminology through the ubiquitous Petersson inner product, a central concept in contemporary research on automorphic representations and arithmetic geometry.

Category:German mathematicians Category:1902 births Category:1984 deaths