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  2. Franz Mertens - Wikipedia

    en.wikipedia.org/wiki/Franz_Mertens

    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 ...

  3. Mertens' theorems - Wikipedia

    en.wikipedia.org/wiki/Mertens'_theorems

    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 .

  4. Franz Carl Mertens - Wikipedia

    en.wikipedia.org/wiki/Franz_Carl_Mertens

    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.

  5. List of mathematicians born in the 19th century - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematicians...

    Franz Mertens (1840–1927) Hermann Minkowski (1864–1909) Emmy Noether (1882–1935) Bernhard Riemann (1826–1866) Arthur Schoenflies (1853–1928) Karl Weierstrass (1815–1897) Hermann Weyl (1885–1955) Richard Dedekind (1831–1916) Friedrich Ludwig Gottlob Frege (1848–1925)

  6. Divergence of the sum of the reciprocals of the primes

    en.wikipedia.org/wiki/Divergence_of_the_sum_of...

    It turns out this is indeed the case, and a more precise version of this fact was rigorously proved by Franz Mertens in 1874. [3] Thus Euler obtained a correct result by questionable means. Erdős's proof by upper and lower estimates

  7. Meissel–Mertens constant - Wikipedia

    en.wikipedia.org/wiki/Meissel–Mertens_constant

    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 Hadamard and Charles Jean de la Vallée-Poussin), or the prime reciprocal constant, is a mathematical constant in number ...

  8. Mertens - Wikipedia

    en.wikipedia.org/wiki/Mertens

    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

  9. Mertens conjecture - Wikipedia

    en.wikipedia.org/wiki/Mertens_conjecture

    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 ...