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In 1961 Wirsing proved a theorem about the asymptotic means of non-negative multiplicative functions, and he was able to show, under certain conditions, that these are essentially determined by their values at the prime numbers (and not also by values at the higher prime exponents). In 1967 he
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He gave in 1962 an elementary proof of a sharpened form of the prime-number theorem (with remainder). (In this context, "elementary" means "not using methods from
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evolution of a random variable evenly distributed in the unit interval. In this context, he also introduced a universal mathematical constant (
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641:, Acta Arithmetica, Vol. 24, 1973/74, pp. 507–562. His results are presented, for example, in
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30:(28 June 1931 – 22 March 2022) was a German mathematician, specializing in number theory.
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Wirsing is also known for his work on the Gauss-Kuzmin-LĂ©vy distribution (named after
57:(On Essential Components in Additive Number Theory). In 1967/68 he was a professor at
410:".) About the same time, similar results were published by Robert Breusch (1960) and
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In 1956, with Alfred Stöhr, Wirsing gave simpler examples (than the example given by
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On the theorem of Gauss-Kuzmin-LĂ©vy and a
Frobenius type theorem for function spaces
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In 1957 he, with
Bernhard Hornfeck, gave an asymptotic estimate for the density of
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255:{\displaystyle \left|\alpha -\beta \right|<H(\beta )^{-(2n+\varepsilon )}}
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600:, Journal für die Reine und Angewandte Mathematik, vol. 196, 1956, pp. 96–98
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648:, Volume 2 (Seminumerical Algorithms), Addison-Wesley, 3rd Edition, p. 363.
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457:"Das asymptotische Verhalten von Summen ĂĽber multiplikative Funktionen".
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In 1960 he proved for algebraic number fields a generalization of
399:. In 1959 Wirsing gave an asymptotic estimate for the density of
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Wirsing organized conferences on analytical number theory at the
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471:"Elementare Beweise des Primzahlsatzes mit Restglied, Part 1".
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Beispiele von wesentlichen
Komponenten, die keine Basis sind
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Approximation mit algebraischen Zahlen beschränkten Grades
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Part 2 in Acta Math. Acad. Sci. Hungar. 18, 1967, 411–447
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497:, J. Number Theory, Vol. 5, 1973, pp. 224–236
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481:(Part 2 vol. 214/215, 1964, pp. 1–18)
334:The exponent on the right was improved to
584:"Traueranzeige Prof. Dr. Eduard Wirsing"
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69:. Since 1974 he was a professor at the
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586:(in German). 26 March 2022. p. 6.
384:in 1942) demonstrating that there are
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658:Gauss-Kuzmin Distribution, Mathworld
38:Wirsing was born on 28 June 1931 in
541:Pietschmann, Peter (14 July 1999).
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728:21st-century German mathematicians
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543:"Emeritiert: Prof. Eduard Wirsing"
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673:photo from University of Marburg
646:The art of computer programming
16:German mathematician (1931–2022)
262:for arbitrarily small positive
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95:, and made electronic devices.
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382:Yuri Linnik
338:(replacing
682:Categories
553:25 January
502:References
486:Alan Baker
352:Paul Erdős
184:, so that
180:of degree
431:Paul LĂ©vy
418:in 1949.
362:−
346:in 1970.
319:β
296:β
270:ε
245:ε
230:−
222:β
205:β
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199:α
168:β
145:≥
125:α
91:, played
34:Biography
635:Wirsing
622:Wirsing
282:, where
110:'s 1955
102:Research
49:and the
570:at the
40:Berlin
484:with
342:) by
89:chess
555:2023
213:<
117:Let
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336:n+1
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