Franz Mertens (20 March 1840 – 5 March 1927) (also known as Franciszek Mertens) was a German-Polish

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. He was born in Schroda in the Grand Duchy of Posen,

Kingdom of Prussia The Kingdom of Prussia (, ) was a German state that existed from 1701 to 1918.Marriott, J. A. R., and Charles Grant Robertson. ''The Evolution of Prussia, the Making of an Empire''. Rev. ed. Oxford: Clarendon Press, 1946. It played a signif ...

(now Środa Wielkopolska,

Poland Poland, officially the Republic of Poland, is a country in Central Europe. It extends from the Baltic Sea in the north to the Sudetes and Carpathian Mountains in the south, bordered by Lithuania and Russia to the northeast, Belarus and Ukrai ...

) and died in

Vienna Vienna ( ; ; ) is the capital city, capital, List of largest cities in Austria, most populous city, and one of Federal states of Austria, nine federal states of Austria. It is Austria's primate city, with just over two million inhabitants. ...

Austria Austria, formally the Republic of Austria, is a landlocked country in Central Europe, lying in the Eastern Alps. It is a federation of nine Federal states of Austria, states, of which the capital Vienna is the List of largest cities in Aust ...

. The Mertens function ''M''(''x'') is the sum function for the

Möbius function The Möbius function \mu(n) is a multiplicative function in number theory introduced by the German mathematician August Ferdinand Möbius (also transliterated ''Moebius'') in 1832. It is ubiquitous in elementary and analytic number theory and m ...

, in the theory of

arithmetic function In number theory, an arithmetic, arithmetical, or number-theoretic function is generally any function whose domain is the set of positive integers and whose range is a subset of the complex numbers. Hardy & Wright include in their definition th ...

s. The Mertens conjecture concerning its growth, conjecturing it bounded by ''x''^1/2, which would have implied the

Riemann hypothesis In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important unsolved problem in pure ...

, 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 and the logarithm is taken twice, not just once. Mertens's theorems are three 1874 results related to the density of prime numbers.

Erwin Schrödinger Erwin Rudolf Josef Alexander Schrödinger ( ; ; 12 August 1887 – 4 January 1961), sometimes written as or , was an Austrian-Irish theoretical physicist who developed fundamental results in quantum field theory, quantum theory. In particul ...

was taught calculus and algebra by Mertens. His memory is honoured by the Franciszek Mertens Scholarship granted (from 2017) to those outstanding pupils of foreign secondary schools who wish to study at the Faculty of Mathematics and Computer Science of the

Jagiellonian University The Jagiellonian University (, UJ) is a public research university in Kraków, Poland. Founded in 1364 by Casimir III the Great, King Casimir III the Great, it is the oldest university in Poland and one of the List of oldest universities in con ...

Kraków , officially the Royal Capital City of Kraków, is the List of cities and towns in Poland, second-largest and one of the oldest cities in Poland. Situated on the Vistula River in Lesser Poland Voivodeship, the city has a population of 804,237 ...

and were finalists of the national-level mathematics, or computer science olympiads, or they have participated in one of the following international olympiads: in

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

(IMO),

computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...

(IOI),

artificial intelligence Artificial intelligence (AI) is the capability of computer, computational systems to perform tasks typically associated with human intelligence, such as learning, reasoning, problem-solving, perception, and decision-making. It is a field of re ...

(IOAI),

astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

(IAO),

astronomy and astrophysics ''Astronomy & Astrophysics (A&A)'' is a monthly peer-reviewed scientific journal covering theoretical, observational, and instrumental astronomy and astrophysics. It is operated by an editorial team under the supervision of a board of directors re ...

(IOAA),

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

(IPhO),

linguistics Linguistics is the scientific study of language. The areas of linguistic analysis are syntax (rules governing the structure of sentences), semantics (meaning), Morphology (linguistics), morphology (structure of words), phonetics (speech sounds ...

(IOL), European Girls' Mathematical Olympiad (EGMO), European Girls’ Olympiad in Informatics (EGOI), Romanian Masters of Mathematics (RMM), Romanian Masters of Informatics (RMI) or International Zhautykov Olympiad (IZhO).

References

External links

* * * {{DEFAULTSORT:Mertens, Franz 1840 births 1927 deaths People from Środa Wielkopolska People from the Province of Posen Mathematicians from the Kingdom of Prussia Polish mathematicians Mathematicians from Austria-Hungary Austrian mathematicians 19th-century German mathematicians 20th-century German mathematicians Humboldt University of Berlin alumni Academic staff of Jagiellonian University Academic staff of the University of Vienna Number theorists

See also

References

External links