Eberhard Freitag (born 19 May 1942, in

Mühlacker Mühlacker is a town in the eastern part of the Enz (district), Enz district of Baden-Württemberg, Germany. Mühlacker station has direct rail connections with Stuttgart, Karlsruhe, Heidelberg, Pforzheim and the Northern Black Forest. Mühlhau ...

) is a German mathematician, specializing in

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

and especially

modular form In mathematics, a modular form is a holomorphic function on the complex upper half-plane, \mathcal, that roughly satisfies a functional equation with respect to the group action of the modular group and a growth condition. The theory of modul ...

Education and career

Freitag studied from 1961 mathematics, physics and astronomy at

Heidelberg University Heidelberg University, officially the Ruprecht Karl University of Heidelberg (; ), is a public research university in Heidelberg, Baden-Württemberg, Germany. Founded in 1386 on instruction of Pope Urban VI, Heidelberg is Germany's oldest unive ...

, where he received in 1964 his

Diplom A ''Diplom'' (, from ) is an academic degree in the German-speaking countries Germany, Austria, and Switzerland and a similarly named degree in some other European countries including Albania, Bulgaria, Belarus, Bosnia and Herzegovina, Croatia ...

and in 1966 his Ph.D. (promotion), supervised by Hans Maaß (and also

Albrecht Dold Albrecht Dold (5 August 1928 – 26 September 2011) was a German mathematician specializing in algebraic topology who proved the Dold–Thom theorem, the Dold–Kan correspondence, and introduced Dold manifolds, Dold–Puppe stabilization, an ...

), with thesis ''Modulformen zweiten Grades zum rationalen und Gaußschen Zahlkörper'', published in Sitzungsberichte Heidelberger Akad. Wiss. 1967. From 1964 he was a research assistant at the Mathematischen Institut in Heidelberg, where he received at the end of 1969 his habilitation and became there a

Privatdozent ''Privatdozent'' (for men) or ''Privatdozentin'' (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualifi ...

and in 1970 a scientific advisor. In 1970–1971 he was a visiting professor at Johann-Wolfgang-Goethe-Universität Frankfurt am Main. In 1973 he became a professor ordinarius at the

University of Mainz The Johannes Gutenberg University Mainz () is a public research university in Mainz, Rhineland Palatinate, Germany. It has been named after the printer Johannes Gutenberg since 1946. it had approximately 32,000 students enrolled in around 100 a ...

. In 1977 he became a professor ordinarius at

, where from 1991 to 1993 he was the dean of the Faculty of Mathematics. Freitag's research (like that of his teacher Maaß) deals primarily with the theory of

s, but approaches modular forms via

algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...

. Among other work, Freitag described this theory in two monographs published by Springer Verlag in Grundlehren der mathematischen Wissenschaften. These two books and the first volume of his series on function theory are standard references. In 1974 in Vancouver he was an Invited Speaker of the ICM with talk ''Singularitäten von Modulmannigfaltigkeiten und Körper Automorpher Funktionen''. In 1998 he proved with Rainer Weissauer and

Richard Borcherds Richard Ewen Borcherds (; born 29 November 1959) is a British mathematician currently working in quantum field theory. He is known for his work in lattices, group theory, and infinite-dimensional algebras,James Lepowsky"The Work of Richard Borch ...

the existence of a Siegel cusp form of degree 12 and weight 12 using the theta series associated with the 24 Niemeier lattices of dimension 24. Freitag also demonstrated that the Siegel modular variety ''A_g'' is of general type when ''g = 8''.

Selected publications

* with Rolf Busam: ''Funktionentheorie 1.'' Springer-Verlag, 1993, 4th edition 2006,
''Complex Analysis'', 2006, Eng. trans. of 4th edition
* ''Funktionentheorie 2: Riemannsche Flächen, Mehrere komplexe Variable, Abelsche Funktionen, Höhere Modulformen'', Springer-Verlag, 2009 * ''Hilbert Modular Forms.'' Springer-Verlag, Grundlehren der mathematischen Wissenschaften, 1990,

* ''Singular Modular Forms and Theta Relations.'' In: ''Lecture Notes in Mathematics.'' vol. 1487, Springer-Verlag, 1991,

* with Reinhardt Kiehl
''Etale Cohomology and the Weil Conjecture''
Springer Verlag, 1988, * ''Siegelsche Modulfunktionen.'' Springer-Verlag, Berlin 1983, Grundlehren der mathematischen Wissenschaften vol. 254,

Sources

* Dagmar Drüll ''Heidelberger Gelehrtenlexikon 1933-1986'', Springer 2009

References

External links

Freitag's homepage at the University of Heidelberg

{{DEFAULTSORT:Freitag, Eberhard 1942 births Living people 20th-century German mathematicians 21st-century German mathematicians Complex analysts Heidelberg University alumni Academic staff of Johannes Gutenberg University Mainz Academic staff of Heidelberg University People from Mühlacker