Eduard Savoy

Eduard Savoy

Eduard Wirsing (born June 28, 1931 in Berlin ) is a German mathematician who mainly deals with number theory.

Life

Wirsing studied at the University of Göttingen and the FU Berlin , where he received his doctorate in 1957 under Hans-Heinrich Ostmann ( on essential components in additive number theory ). 1967/68 he was a professor at Cornell University and from 1969 professor at the Philipps University of Marburg , where he had been since 1965. In 1970/71 he was at the Institute for Advanced Study . Since 1974 he was a professor at the University of Ulm , where he headed the Mathematical Colloquium from 1976. He retired in 1999, but remained scientifically active.

He organized conferences on analytical number theory at the Oberwolfach Mathematical Research Institute .

In his free time he plays go and chess, plays the treble recorder and tinkers with electronic devices.

plant

In 1960 he proved a version of Roth's theorem (1955) for algebraic number fields:

Let be algebraic of degree , then there are only finitely many algebraic numbers of degree n and height H such that ${\displaystyle \alpha }$ ${\displaystyle \geq 3}$ ${\displaystyle \beta }$

${\displaystyle \left|\alpha -\beta \right|<H^{-(2n+\varepsilon )}}$

for any small positive . The exponent on the right was improved by Wolfgang M. Schmidt in 1970 (n + 1 instead of 2n). ${\displaystyle \varepsilon }$

In 1961 he proved a theorem about the asymptotic mean values ​​of non-negative multiplicative functions, where he succeeded under certain conditions to show that these are essentially determined by their values ​​on the prime numbers (and not also by values ​​on the higher prime exponents). In 1967 he tightened his theorem even further and was able to prove a conjecture by Paul Erdős (every multiplicative function that only takes the values ​​1 and −1 has a mean).

In the late 1950s he gave accurate estimates of the asymptotic behavior of the density of perfect numbers .

In 1956 he gave a simpler example with Alfred Stöhr (than Juri Linnik in 1942) that there are essential components that are not a basis.

In 1962 he gave an elementary proof of an intensified form of the prime number theorem (with remainder). Elementary proofs of the prime number theorem were first given by Paul Erdős and Atle Selberg in 1949.

Wirsing is also known for his work on the Gauss-Kusmin-Levy distribution (after Carl Friedrich Gauss , Rodion Ossijewitsch Kusmin , Paul Lévy ). These are asymptotic estimates for the distribution of the coefficients of the regular continued fraction expansion of a random variable evenly distributed in the unit interval. In this context he also introduced a universal mathematical constant (Gauss-Kusmin-Wirsing constant) (see mathematical constant ).

Fonts

• Approximation with algebraic numbers of limited degree , Journal für Reine und Angewandte Mathematik, Volume 206, 1961, pp. 67-77
• The asymptotic behavior of sums over multiplicative functions, Mathematische Annalen, Volume 143, 1961, pp. 7-103, part 2 in Acta Math. Acad. Sci. Hungar. 18, 1967, 411-447
• Elementary proofs of the prime number theorem with remainder, Part 1, Journal für Reine und Angewandte Mathematik, Volume 211, 1962, pp. 205–214 (Part 2, Volume 214/215, 1964, pp. 1–18)
• with Alan Baker , Bryan Birch On a problem of Chowla , J. Number Theory, Vol. 5, 1973, pp. 224-236

literature

• Andrzej Schinzel , Wolfgang M. Schmidt The mathematical work of Eduard Wirsing , Functiones et Approximatio Commentarii Mathematici, Volume 35, 2006, pp. 7-18

Web links

• Photo in Marburg

Individual evidence

1. ↑ University protocols 1999 on retirement
2. ^ Mathematics Genealogy Project
3. ↑ Wirsing comment on the work on perfect numbers , Mathematische Annalen, Volume 137, 1959, pp. 316-318, before that Wirsing, Hornfeck on the frequency of perfect numbers , Mathematische Annalen, Volume 133, 1957, pp. 431-438
4. ↑ Set of natural numbers which, if they are added to a set of numbers with positive density, always increases its density. According to Erdős, all bases are essential components.
5. ↑ Stöhr, Wirsing Examples of essential components that are not a basis , Journal für Reine und Angewandte Mathematik, Volume 196, 1956, pp. 96-98
6. ↑ About the same time R. Breusch (1960) and Enrico Bombieri (1962)
7. ↑ Wirsing On the theorem of Gauss-Kusmin-Lévy and a Frobenius type theorem for function spaces , Acta Arithmetica, Volume 24, 1973/74, pp. 507-62. Its results are z. B. in Donald Knuth The art of computer programming , Volume 2 (Seminumerical Algorithms), Addison-Wesley, 3rd edition, p. 363ff
8. ^ Gauss-Kuzmin Distribution, Mathworld