Franz Mertens

Franz Mertens (March 20, 1840 - March 5, 1927) was a German mathematician. He was born in ?roda in the Grand Duchy of Pozna?, Kingdom of Prussia (now ?roda Wielkopolska, Poland) and died in Vienna, Austria.

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March 20 - 1840 - March 5 - 1927 - German - Mathematician - ?roda - Grand Duchy of Pozna? - Kingdom of Prussia - Poland - Vienna - Austria

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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.

Related Topics:
Mertens function - Möbius function - Arithmetic function - Mertens conjecture - Riemann hypothesis - Odlyzko - Meissel-Mertens constant - Euler-Mascheroni constant - Harmonic series - Primes

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See also: Mertens' theorems.

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