Editing Franz Mertens

{{Short description|Polish-Austrian mathematician}}
{{Infobox scientist
| name              = Franz Mertens
| image             = Franz Mertens.jpg
| image_size        =
| caption           =
| birth_date        = {{birth date|1840|3|20|df=y}}
| birth_place       = [[Środa Wielkopolska|Schroda]], [[Kingdom of Prussia|Prussia]]
| death_date        = {{death date and age|1927|3|5|1840|3|20|df=y}}
| death_place       = [[Vienna]], [[Republic of Austria (1919–1934)|Austria]]
| nationality       = [[Poland|Polish]]
| fields            = [[Mathematics]]
| workplaces        = [[University of Vienna]] <br> [[Graz University of Technology|Graz Polytechnic]] <br> [[Jagiellonian University]]
| alma_mater        = [[University of Berlin]]
| doctoral_advisor  = [[Ernst Eduard Kummer]]<br>[[Leopold Kronecker]]
| doctoral_students = [[Ernst Sigismund Fischer|Ernst S. Fischer]]<br>[[Eduard Helly]]
| known_for         = [[Mertens conjecture]]<br>[[Mertens function]]<br>[[Meissel–Mertens constant]]<br>[[Mertens's theorems]]
| awards            =
}}
'''Franz Mertens''' (20 March 1840 – 5 March 1927) (also known as '''Franciszek Mertens''') was a German-Polish [[mathematician]]. He was born in [[Środa Wielkopolska|Schroda]] in the [[Grand Duchy of Posen]], [[Kingdom of Prussia]] (now [[Środa Wielkopolska]], [[Poland]]) and died in [[Vienna]], [[First Austrian Republic|Austria]].

The [[Mertens function]] ''M''(''x'') is the sum function for the [[Möbius function]], in the theory of [[arithmetic function]]s. The [[Mertens conjecture]] concerning its growth, conjecturing it bounded by ''x''<sup>1/2</sup>, which would have implied the [[Riemann hypothesis]], is now known to be false ([[Andrew Odlyzko|Odlyzko]] and [[Herman te Riele|te Riele]], 1985).  The [[Meissel–Mertens constant]] is analogous to the [[Euler–Mascheroni constant]], but the [[harmonic series (mathematics)|harmonic series]] sum in its definition is only over the [[prime number|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]] was taught calculus and algebra by Mertens.<ref>{{cite web|title=Erwin Schrödinger biography|url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Schrodinger.html}}</ref>

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]] in [[Kraków]] and were finalists of the [[List of mathematics competitions#National mathematics olympiads|national-level mathematics]], or computer science olympiads, or they have participated in one of the following international olympiads: in [[International Mathematical Olympiad|mathematics]] (IMO), [[International Olympiad in Informatics|computer science]] (IOI), [[International Olympiad in Artificial Intelligence|artificial intelligence]] (IOAI), [[International Astronomy Olympiad|astronomy]] (IAO), [[International Olympiad on Astronomy and Astrophysics|astronomy and astrophysics]] (IOAA), [[International Physics Olympiad|physics]] (IPhO), [[International Linguistics Olympiad|linguistics]] (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).<ref>{{Cite web|url=http://www.matinf.uj.edu.pl/en_GB/kandydaci/oferta-dla-najlepszych/stypendium-mertensa|title=Franciszek Mertens Scholarship|access-date=2024-05-04}}</ref>

==See also==
* [[Mertens's theorems]]
* [[Cauchy product]]

==References==
{{reflist}}

==External links==
*{{Commons category-inline}}
* {{MacTutor Biography|id=Mertens}}
* {{MathGenealogy|id=49524}}

{{Authority control}}

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