Franz Mertens

Mathematician, Academic

1840 – 1927

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Who was Franz Mertens?

Franz Mertens was a German mathematician. He was born in Schroda in the Grand Duchy of Posen, 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. 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. Mertens' theorems are three 1874 results related to the density of prime numbers.

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Born
Mar 20, 1840
Środa Wielkopolska
Nationality
  • Germany
Profession
Education
  • Humboldt University of Berlin
Died
Mar 5, 1927
Vienna

Submitted
on July 23, 2013

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