Franz Mertens (mathematician)
Franz (Franciszek) Carl Josef Mertens (born March 20, 1840 in Schroda , Province of Posen , † March 5, 1927 in Vienna ) was a Polish - Austrian mathematician .
Franz Mertens studied in Berlin and obtained his doctorate in 1865 through a dissertation on potential theory with Ernst Eduard Kummer and Leopold Kronecker . He dealt with number theory throughout his life and is perhaps best known for a simplified proof of Dirichlet's prime number theorem .
In 1865 he became an associate professor and in 1870 a full professor at the Jagiellonian University in Krakow . From 1884 he was professor at the Polytechnic in Graz and from 1894 full professor for mathematics at the University of Vienna . In 1911 he retired, but continued to give lectures.
His honorary grave is located in the Vienna Central Cemetery (30D-2-5).
His students in Vienna include Ernst Sigismund Fischer , Eduard Helly and Erwin Schrödinger .
On the question of the distribution of prime numbers , he put forward Mertens' three theorems . The Mertens function named after him arises as a summation of the Möbius function . The Mertens conjecture says that this function is bounded by , from which the Riemann conjecture would follow. In 1985 Andrew Odlyzko and Herman te Riele were able to refute the Mertens conjecture.
- Corresponding member of the Göttingen learned society
- Foreign member of the Kraków kk Academy of Sciences
- Corresponding member of the Royal Bohemian Society of Sciences
- Corresponding member of the Austrian Academy of Sciences (1892)
- full member of the Austrian Academy of Sciences (1894)
- corresponding member of the Prussian Academy of Sciences (1900)
- Meissel-Mertens constant
- Mertens theorem (Cauchy product)
- Mertens theorem (resultant system)
- Mertens theorem (number theory)
- Constantin von Wurzbach : Mertens, Franz Karl Joseph . In: Biographisches Lexikon des Kaiserthums Oesterreich . 17th part. Kaiserlich-Königliche Hof- und Staatsdruckerei, Vienna 1867, p. 410 ( digitized version ).
- Hans Hornich : Mertens Franz. In: Austrian Biographical Lexicon 1815–1950 (ÖBL). Volume 6, Verlag der Österreichischen Akademie der Wissenschaften, Vienna 1975, ISBN 3-7001-0128-7 , p. 235.
- Gottlob Kirschmer: Mertens, Franz. In: New German Biography (NDB). Volume 17, Duncker & Humblot, Berlin 1994, ISBN 3-428-00198-2 , p. 183 ( digitized version ).
- John J. O'Connor, Edmund F. Robertson : Franz Mertens (mathematician). In: MacTutor History of Mathematics archive .
- Franz Mertens in the Mathematics Genealogy Project
- Entry about Mertens, Franz in the Austria-Forum (biography)
- ↑ Franciszek Mertens ( Memento of the original from March 3, 2016 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.
- ↑ Weitz / HAW Hamburg: Mathematics is more than arithmetic - example: Mertens' hypothesis on YouTube , accessed on March 22, 2020.
- ^ Members of the previous academies. Franz Mertens. Berlin-Brandenburg Academy of Sciences and Humanities , accessed on May 6, 2015 .
|ALTERNATIVE NAMES||Mertens, Franz Carl Josef (full name)|
|BRIEF DESCRIPTION||Austrian mathematician|
|DATE OF BIRTH||March 20, 1840|
|PLACE OF BIRTH||Schroda, today Środa Wielkopolska , Province of Poznan|
|DATE OF DEATH||March 5, 1927|
|Place of death||Vienna|