Franz Mertens
Franz Mertens was a German-Polish mathematician. He was born in Schroda in the Grand Duchy of Posen, Kingdom of Prussia and died in Vienna, Austria.
The Mertens function M is the sum function for the Möbius function, in the theory of arithmetic functions. The Mertens conjecture concerning its growth, conjecturing it bounded by x1/2, which would have implied the Riemann hypothesis, is now known to be false. 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's theorems are three 1874 results related to the density of prime numbers.
Erwin Schrödinger was taught calculus and algebra by Mertens.
His memory is honoured by the Franciszek Mertens Scholarship granted to those outstanding pupils of foreign secondary schools who wish to study at the Faculty of Mathematics and Computer Science of the Jagiellonian University in Kraków and were finalists of the mathematics competitions#National mathematics olympiads|national-level mathematics], or computer science olympiads, or they have participated in one of the following international olympiads: in International [Mathematical Olympiad|mathematics], computer science, artificial intelligence, astronomy, astronomy and astrophysics, International [Physics Olympiad|physics], linguistics, European Girls' Mathematical Olympiad, European Girls’ Olympiad in Informatics, Romanian Masters of Mathematics, Romanian Masters of Informatics or International Zhautykov Olympiad.