Franz Mertens (March 20, 1840 - March 5, 1927) was a German mathematician. Events 1600 - The Linköping Bloodbath takes place on Maundy Thursday in Linköping, Sweden. Year 1840 ( MDCCCXL) was a Leap year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Leap year Events 363 - Roman Emperor Julian moves from Antioch with an army of 90000 to attack the Sassanid Empire, in a Year 1927 ( MCMXXVII) was a Common year starting on Saturday (link will display full calendar of the Gregorian calendar. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. A mathematician is a person whose primary area of study and research is the field of Mathematics. He was born in Środa in the Grand Duchy of Poznań, Kingdom of Prussia (now Środa Wielkopolska, Poland) and died in Vienna, Austria. Środa Wielkopolska (Schroda is a town in central Poland, about 30 km southeast of Poznań, with 21631 inhabitants ( 2004) The Grand Duchy of Posen (Großherzogtum Posen Wielkie Księstwo Poznańskie was an autonomous province of the Kingdom of Prussia in the Polish lands commonly known as " The Kingdom of Prussia (Königreich Preußen was a German kingdom from 1701 to 1918 and from 1871 was the leading state of the German Empire, comprising Poland (Polska officially the Republic of Poland Vienna ( in Wien; see also other names) is the Capital of Austria, and is also one of the nine States of Austria. Austria (Österreich ( officially the Republic of Austria (Republik Österreich
The Mertens function is the sum function for the Möbius function, in the theory of arithmetic functions. In Number theory, the Mertens function is M(n = \sum_{1\le k \le n} \mu(k where μ(k is the Möbius function. For the rational functions defined on the complex numbers see Möbius transformation. In Number theory an arithmetic function or arithmetical function is a Function defined on the set of Natural numbers (i 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). In Mathematics, the Mertens conjecture is a statement about the behaviour of a certain function as its argument increases The Riemann hypothesis (also called the Riemann zeta-hypothesis) first formulated by Bernhard Riemann in 1859 is one of the most famous and important unsolved Andrew Odlyzko is a mathematician who is the head of the University of Minnesota 's Digital Technology Center 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. The Meissel-Mertens constant, also referred to as Mertens constant, Kronecker's constant, Hadamard-de la Vallée-Poussin constant or prime reciprocal The Euler–Mascheroni constant (also called the Euler constant) is a Mathematical constant recurring in analysis and Number theory, usually See Harmonic series (music for the (related musical concept In Mathematics, the harmonic series is the Infinite series In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1
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External links
- O'Connor, John J. In Mathematics, Mertens' theorems are three 1874 results in Number theory related to the density of Prime numbers and one result in analysis & Robertson, Edmund F. , “Franz Mertens”, MacTutor History of Mathematics archive
- Franz Mertens at the Mathematics Genealogy Project