### Quick Info

Born
26 June 1902
Bentschen, Posen, Germany (now Poznań, Poland)
Died
9 November 1984
Münster, Germany

Summary
Hans Petersson was a German mathematician who worked in the theory of modular and automorphic forms.

### Biography

Petersson studied for his doctorate at Hamburg University where his studies in algebraic number theory were supervised by Hecke. After the award of his doctorate in 1925 for the thesis Über die Darstellung natürlicher Zahlen durch definite und indefinite quadratische Formen von 2r Variablen he remained at Hamburg, continuing to study with Hecke, and the successful submission of his habilitation thesis to Hamburg in 1929 saw him become a Privatdozent there. On 30 January 1933 the National Socialist party led by Hitler came to power in Germany. Petersson was an Aryan so was not affected by the Civil Service Law, passed on 7 April 1933, which provided the means of removing Jewish teachers from the universities. However Petersson married Margarete Ehlers on 30 September 1933 and his wife had a Jewish grandparent on her mother's side. Petersson asked Hecke for advice and he suggested that he join the Sturmabteilung (Stormtroopers). Although Petersson had a strong dislike for the National Socialists, he acted out of self-preservation.

Hecke, Blaschke and Artin, all professors at Hamburg, requested Petersson's promotion on 8 June 1934. However the request was refused on the grounds that promotion was only possible after teaching for six years. Petersson was now in a difficult financial position, only being a Privatdozent but having to support a wife. He tried to find a professorship by approaching Hans-Heinrich Lammers, the Secretary of State, who had been a friend of his father. Lammers sent Petersson's request to be considered for a chair to the Ministry of Education who asked three known Nazi supporters Tornier, Bieberbach and Riebesell for their opinions. The Ministry of Education, having received reasonable but not particularly strong references, decided not to offer Petersson a chair.

Blaschke tried to obtain a chair for Petersson in Calcutta in 1935 but was unsuccessful. Having now satisfied the six years teaching experience criterion, an application went in from Hamburg for Petersson's promotion in June 1935. This time Bieberbach, Hecke, and Hasse were asked for opinions and on 4 December Petersson was asked to supply birth certificates giving his religion and marriage certificates for himself and his wife going back two generations. He said that as Bentschen was now Polish these could not all be given and he managed to hide the non-Aryan relations on his wife's side. Certainly his membership of the Stormtroopers helped prevent investigation as he had hoped.

On 1 May 1937 Petersson joined the Nazi party, after a lengthy explanation of why his name was not given a German spelling, still trying to gain favour. In this he was certainly successful. A report by the Hamburg division of the Nazi party reported in April 1938 [1]:-
The information requested from his Sturmabteilung naval groups about Petersson has turned out very good. Besides Petersson has been a party member since 1 May 1937. Petersson in the meantime has likewise completed an eight-week military exercise. Professor Petersson represents the rarely occurring case of a mathematician who stands without reservation on the ground of the National Socialists and besides is active in the Sturmabteilung with a will.
On 9 September 1939 he was appointed to a chair at Prague University but, perhaps due to the war starting, did not now want to leave Hamburg. On 7 October 1940 he was ordered to Prague. In 1941 he went to Strasbourg University and worked there until 1944 when the advancing armies of the allies forced the closure of the university. Blaschke requested that Petersson return to Hamburg. At the end of World War II in 1945 he was suspended and investigated by the denazification committee. They were made aware of the reasons for which Petersson had joined the Stormtroopers and noted that he had not been:-
... very active in the Stormtroopers [for] during twelve years of membership he did not reach a rank higher than private first class.
Petersson was reinstated in Hamburg in March 1947. He turned down offers of professorships at Jena and Rostock in 1951, possibly because they were in East Germany. He accepted an appointment as ordinary professor at Münster in 1953 and remained there for the rest of his career. From 1953 until his retirement in the year 1970 he was a director of the Mathematical Institute of the Westfälischen Wilhelms University at Münster.

Petersson's leading contributions to the theory of modular and automorphic forms began with the introduction in 1939 of his inner product as a tool for studying these functions. As noted in [2]:-
... the abstract notion of a vector space appeared in print only in 1922 in papers by S Banach and H Hahn.
So what is now completely standard linear algebra for all mathematicians was, when Petersson published Konstruktion der sämtlichen Lösungen einer Riemannschen Funktionalgleichung durch Dirichlet-Reihen mit Eulerscher Produktentwicklung in 1939, at the forefront of the latest research.

In 1982 Petersson published an important book Modulfunktionen und quadratische Formen in Springer-Verlag's Ergebnisse der Mathematik und ihrer Grenzgebiete series. Fomenko, reviewing the book, writes:-
This book is a detailed introduction to the theory of elliptic modular forms and relies on the classical works of Hecke and of the author. It is concerned with the study of the representation of integers by positive-definite quadratic forms by means of the theory of modular forms, in particular, of the theory of theta-functions. The basic aim of this book is to evaluate (in explicit form) the number of representations of integers $n$ by specific positive-definite quadratic forms F.
Petersson continued to undertake important research after he retired in 1970 and his final paper Über Spuren von Modulformen und die Eisensteinschen Reihen in den Kongruenzklassen der rationalen Modulgruppe appeared in 1986, two years after his death.

### References (show)

1. S L Segal, Mathematicians under the Nazis (Princeton, 2003).
2. J Elstrodt and F Grunewald, The Petersson scalar product, Jahresber. Deutsch. Math.-Verein. 100 (4) (1998), 253-283.
3. K Wohlfahrt, Hans Petersson zum Gedächtnis, Jahresber. Deutsch. Math.-Verein. 96 (3) (1994), 117-129.