Franz Mertens (mathematician)

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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


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.


See also


Web links

Individual evidence

  1. 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.  @1@ 2Template: Webachiv / IABot /
  2. Weitz / HAW Hamburg: Mathematics is more than arithmetic - example: Mertens' hypothesis on YouTube , accessed on March 22, 2020.
  3. ^ Members of the previous academies. Franz Mertens. Berlin-Brandenburg Academy of Sciences and Humanities , accessed on May 6, 2015 .