Franz Mertens

Franz Mertens was a German mathematician, born: March 20, 1840, Schroda near Posen, Kingdom of Prussia (now Sroda, Poland), died: March 5, 1927, Vienna, Austria.

The Mertens function 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).

See also: Meissel-Mertens constant