Franz Mertens

Franz Mertens
File:Franz Mertens.jpg
Born	(1840-03-20)20 March 1840 Środa Wielkopolska, Prussia
Died	Vienna, Austria
Nationality	Germany
Fields	Mathematics
Institutions	University of Vienna Jagiellonian University
Alma mater	University of Berlin
Doctoral advisor	Ernst Eduard Kummer Leopold Kronecker
Doctoral students	Ernst S. Fischer Eduard Helly Tonio Rella
Known for	Mertens function Meissel–Mertens constant Mertens' theorems

Franciszek (Franz) Mertens (20 March 1840 – 5 March 1927) was a Polish-Austrian mathematician. He was born in Środa Wielkopolska in the Grand Duchy of Poznań, Kingdom of Prussia and died in Vienna, Austria.

The Mertens function M(x) is the sum function for the Möbius function, in the theory of arithmetic functions. The Mertens conjecture concerning its growth, conjecturing it bounded by x^1/2, which would have implied the Riemann hypothesis, is now known to be false (Odlyzko and te Riele, 1985). The Meissel–Mertens constant is analogous to the Euler–Mascheroni constant, but the harmonic series sum in its definition is only over the primes rather than over all integers and the logarithm is taken twice, not just once. Mertens' theorems are three 1874 results related to the density of prime numbers.

Erwin Schrödinger was taught calculus and algebra by Mertens.

External links

• .
• Franz Mertens at the Mathematics Genealogy Project