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Franz Mertens (20 March 1840 – 5 March 1927) (also known as Franciszek Mertens) was a Polish mathematician. He was born in Schroda in the Grand Duchy of Posen, Kingdom of Prussia (now Środa Wielkopolska, Poland) and died in Vienna, Austria. The Mertens function M(x) is the sum function for the Möbius function, in the theory of arithmetic ...
Franz Carl Mertens (3 April 1764 – 19 June 1831) was a German botanist who was a native of Bielefeld. He specialized in the field of phycology . Mertens studied theology and languages at the University of Halle , and after graduation taught classes at Bremen Polytechnic College.
In analytic number theory, Mertens' theorems are three 1874 results related to the density of prime numbers proved by Franz Mertens. [ 1 ] In the following, let p ≤ n {\displaystyle p\leq n} mean all primes not exceeding n .
In mathematics, the Mertens conjecture is the statement that the Mertens function is bounded by . Although now disproven, it had been shown to imply the Riemann hypothesis . It was conjectured by Thomas Joannes Stieltjes , in an 1885 letter to Charles Hermite (reprinted in Stieltjes ( 1905 )), and again in print by Franz Mertens ( 1897 ), and ...
Mertens (Dutch pronunciation: [ˈmɛrtəns]) is a surname of Flemish origin, meaning "son of Merten" . It is the fifth most common name in Belgium with 18,518 people in 2008. Geographical distribution
The function is named in honour of Franz Mertens. This definition can be extended to positive real numbers as follows: = (⌊ ⌋). Less formally, () is the count of square-free integers up to x that have an even number of prime factors, minus the count of those that have an odd number.
In the limit, the sum of the reciprocals of the primes < n and the function ln(ln n) are separated by a constant, the Meissel–Mertens constant (labelled M above). The Meissel–Mertens constant (named after Ernst Meissel and Franz Mertens), also referred to as the Mertens constant, Kronecker's constant (after Leopold Kronecker), Hadamard–de la Vallée-Poussin constant (after Jacques ...
Pierre Mertens (9 October 1939 – 19 January 2025) was a Belgian writer and lawyer who specialised in international law, director of the Centre de sociologie de la littérature at the Université Libre de Bruxelles, and literary critic with the newspaper Le Soir.