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 x1/2, 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.
In the years 1853-1860, Franciszek Mertens was a student of the high school in Trzemszno, another town of the Poznan region and then in the 1860-1864 studied mathematics at the University of Berlin which in that era was one of the leading mathematical centers.
The breakthrough year for Mertens was 1874 when two papers of his on the analytical theory of numbers appeared in the afore mentioned journal and constituted, augmented by later published work on related topics, a significant advance in the field.
Mertens' soujourn at the Jagiellonian University coincided with the repolonization of the university and that means that the matter about Auguste Dick wrote "Mertens sorach und schrieb Deutsch and Polnisch gleich gut" which equates his knowledge of Polish and German, had considerable importance.
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