The 1960 generalization of the Thue-Siegel-Roth theorem for algebraic number fields remains a defining achievement of the German number theorist Eduard Wirsing. His work throughout the latter half of the twentieth century focused on analytical number theory, shifting focus from complex function theory toward elementary methods, significantly influencing the density estimates for perfect numbers and multiplicative functions.
Academic Trajectory
Eduard Wirsing was born in Berlin in 1931. He completed his doctoral studies in 1957 at the Freie Universität Berlin under the guidance of Hans-Heinrich Ostmann, following time spent at the University of Göttingen. His thesis, which analyzed essential components in additive number theory, established his professional trajectory. By 1965, he became a professor at the University of Marburg, where he maintained his position through 1969. During his career, he served as a professor at Cornell University and, beginning in 1974, he joined the faculty at Ulm University. He retired as professor emeritus in 1999 but remained active in his research field until his death in Cologne in 2022.
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Wirsing made several advancements regarding asymptotic estimates. In 1957, alongside Bernhard Hornfeck, he calculated the density of perfect numbers, followed by an estimate for multiply perfect numbers in 1959. Working with Alfred Stöhr in 1956, he provided examples of essential components that fail to function as additive bases. His 1961 theorem on multiplicative functions proved that the asymptotic means of these non-negative functions are largely determined by values at prime numbers. He later sharpened this work in 1967 to prove a conjecture posed by Paul Erdős regarding multiplicative functions that alternate between 1 and -1.
Methodological Shifts and Constants
In 1962, Wirsing published an elementary proof regarding the prime-number theorem with remainder, intentionally avoiding complex function theory. His interest in analytical number theory led him to organize various conferences at the Oberwolfach Research Institute for Mathematics. Beyond prime theory, he analyzed the Gauss-Kuzmin-Lévy distribution, which concerns continued fraction evolution. This investigation resulted in the introduction of a universal mathematical constant now identified as the Gauss-Kuzmin-Wirsing constant. Outside of his professional research, Wirsing pursued technical hobbies including chess, playing the alto recorder, and constructing electronic hardware.
Fast facts
- Born: 1931, Berlin
- Died: 2022, Cologne
- Doctoral supervisor: Hans-Heinrich Ostmann
- Primary field: Number theory
- Key academic tenure: Ulm University (1974-1999)
- Notable contribution: Gauss-Kuzmin-Wirsing constant
- Languages: English
Questions readers ask
What is the Gauss-Kuzmin-Wirsing constant?
It is a mathematical constant derived from Wirsing's work on the asymptotic estimates of continued fraction evolution.
Did Wirsing use complex function theory for his proof of the prime-number theorem?
No, he utilized elementary methods, meaning he avoided the use of complex function theory.
Achievements
- Held posts at University of Marburg and Ulm University
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