Franz Mertens

Franz Mertens (20 March 1840 to 5 March 1927), also known as Franciszek Mertens, was a German-Polish mathematician, born in Schroda in the Grand Duchy of Posen, Kingdom of Prussia, now Środa Wielkopolska in Poland, who died in Vienna, Austria. The Mertens function M(x) is the sum function for the Möbius function in the theory of arithmetic functions, and the Mertens conjecture on its growth, which would have implied the Riemann hypothesis, is now known to be false. The Meissel-Mertens constant is also named after him, as are Mertens's theorems, three results of 1874 related to the density of prime numbers. Erwin Schrödinger was taught calculus and algebra by Mertens.