# 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

## Life

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 .

## plant

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. ${\ displaystyle {\ sqrt {x}}}$