Franz Mertens
| Franz Mertens | |
|---|---|
 | |
| Born |
20 March 1840 Środa Wielkopolska, Prussia |
| Died |
5 March 1927 (aged 86) 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[1]-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 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 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.[2]
References
External links
- O'Connor, John J.; Robertson, Edmund F., "Franz Mertens", MacTutor History of Mathematics archive, University of St Andrews.
- Franz Mertens at the Mathematics Genealogy Project
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