Hans Maass

{{Short description|German mathematician (1911–1992)}} {{Multiple issues| {{No footnotes|date=May 2023}} {{More citations needed|date=May 2026}} }} thumb|right|Hans Maass (1969) '''Hans Maass''' ({{langx|de|Hans Maaß}}; June 17, 1911, in Hamburg – April 15, 1992) was a German mathematician who introduced Maass wave forms {{harv|Maass|1949}} and Koecher–Maass series {{harv|Maass|1950}} 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, 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==

*{{Citation | last1=Maass | first1=Hans | authorlink=Hans Maass|title=Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen | doi=10.1007/BF01329622 | mr=0031519 | year=1949 | journal=Mathematische Annalen | issn=0025-5831 | volume=121 | pages=141–183| s2cid=119494842 }} * Maass, H. (1949), "Automorphe Funktionen von mehreren Veranderlichen und Dirichletsche Reihen", ''Abhandlungen aus dem Mathematischen Seminar der Universit%C3%A4t Hamburg'' 16:72–100. *{{Citation | last1=Maass | first1=Hans | title=Modulformen zweiten Grades und Dirichletreihen | doi=10.1007/BF01342953 | mr=0037870 | year=1950 | journal=Mathematische Annalen | issn=0025-5831 | volume=122 | pages=90–108| s2cid=121901325 }} *{{Citation | last1=Maass | first1=Hans | title=On Siegel's Modular Functions | url=http://www.math.tifr.res.in/~publ/ln/tifr03.pdf | series=Tata Institute of Fundamental Research Lectures on Mathematics | year=1955 | volume=3}} *{{Citation | last1=Maass | first1=Hans | editor1-last=Lal | editor1-first=Sunder | title=Lectures on modular functions of one complex variable | url=http://www.math.tifr.res.in/~publ/ln/tifr29.pdf | publisher=Tata Institute of Fundamental Research | location=Bombay | series=Tata Institute of Fundamental Research Lectures on Mathematics | isbn=978-3-540-12874-8 | year=1964 | volume=29 | mr=0218305}} *{{Citation | last1=Maass | first1=Hans | title=Siegel's Modular Forms and Dirichlet Series | publisher=Springer-Verlag | location=Berlin, New York | series=Lecture Notes in Mathematics | doi=10.1007/BFb0058625 |mr=0344198 | year=1971 | volume=216| isbn=978-3-540-05563-1 }}

==References==

*{{Citation | last1=Busam | first1=R. | last2=Freitag | first2=E. | title=Hans Maass(17. 6. 1911-15. 4. 1992) | url=http://dml.math.uni-bielefeld.de/JB_DMV/JB_DMV_101_3.ocr.djvu | mr=1713154 | year=1999 | journal=Jahresbericht der Deutschen Mathematiker-Vereinigung | issn=0012-0456 | volume=101 | issue=3 | pages=135–150}}

==External links== * {{wikiquote-inline}}

{{Authority control}} {{DEFAULTSORT:Maass, Hans}} Category:20th-century German mathematicians Category:1911 births Category:1992 deaths Category:National Socialist Motor Corps members