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Franciszek (Franz) Mertens (20 March 1840 – 5 March 1927) was a Polish-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).

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  • Franciszek (Franz) Mertens (20 March 1840 – 5 March 1927) was a Polish-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).
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  • Franz Mertens
  • Mertens, Franz
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  • German mathematician
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