Adolf Piltz

Adolf Piltz (born December 8, 1855 in Ilmenau , † 1940 near Großheringen ) was a German mathematician who worked in the field of number theory .

Life

The Piltz divider problem in his doctoral thesis from 1881

Adolf Piltz attended grammar school in Eisenach and, after military service in 1875/76, studied in Jena and Berlin. After the teacher's exam in 1881, he was a trainee lawyer at the Wittstock grammar school in 1881/82 . In 1883 he completed his habilitation with Carl Johannes Thomae at the University of Jena , where he applied for a position as a private lecturer. The Faculty's report contained the note that Dr. It takes Piltz a great deal of work to express his knowledge and thoughts. Nevertheless, his application was accepted and he worked as a private lecturer in Jena from 1883 to 1897. From 1884 he was also a member of the Jena Society for Medicine and Science .

After the death of his father, who had previously supported him financially, Adolf Piltz had to give up his (unpaid) lectureship in 1897 (after a scandal, to which a report by the psychiatrist Otto Binswanger contributed, which, for example, spoke of "years of wasting time" by the private lecturer) . After that, Piltz was editor of the "Thuringian Courier" in Bad Sulza until 1926 and at times taught mathematics at the Thuringian technical center in Ilmenau. In 1940 he drowned on large herring in the Ilm .

The Piltz divider problem , which is a generalization of the Dirichlet divider problem, is named after Adolf Piltz . In 1901 Piltz wrote two letters to Edmund Landau (Berlin, from 1909 in Göttingen) in which he wanted to make an earlier announcement of an improved result for Dirichlet's divider problem (see Landau's work On Dirichlet's divider problem from 1920). Although Landau found Piltz's argument incomprehensible, he was able to take up his approach and even described it as an “ingenious method” ( On Dirichlet's divider problem , p. 16).

Fonts

Doctoral thesis: On the law according to which the mean representability of natural numbers as products of a given number of factors increases with the size of the numbers , Berlin, 1881 ( Göttingen Digitization Center )
Habilitation thesis: About the frequency of prime numbers in arithmetic progressions and related laws , Neuenhahn, Jena, 1884 ( online )
Communication on the three-body problem , annual report of DMV 1 , 68–70, 1890/91
A communication from number theory , Naturf. Ges. Halle 64 , 15-16, 1891

literature

Matthias Steinbach : … lost all hold through years of swamping…, Adolf Piltz (1855-1940) , in: M. Steinbach, M. Ploenus (eds.): Ketzer, Käuze, Querulanten. Outsider in the university environment , Dr. Bussert & Stadeler Verlag, Jena, 2008, pp. 198–212
Edmund Landau : About Dirichlet's divider problem , Nachrichten Gesell. Knowledge Göttingen, 13–32, 1920 ( online )
Johannes van der Corput : Number-theoretical estimations according to the Piltz method , Math. Z. 10 , 105-120, 1921
Harald Cramér : About the dividing problem by Piltz , Ark. for Mat., Astron. och Fys. 16, No. 21, 1922 (40 pages)
Gábor Szegő , Arnold Walfisz : About the Piltz divider problem in algebraic number fields. (First paper) , Math. Z. 26 , 138–156, 1927
Ekkehard Krätzel : Theory of Grid Points , Elements of Mathematics 47 , 6-18, 1992 (especially p. 15) ( online )

Web links

Entry in the Mathematics Genealogy Project
Lothar Kreiser: Gottlob Frege: Life, Work, Time , Meiner Verlag, Hamburg, 2001

Individual evidence

^ And simultaneous doctorate supervised by Ernst Kummer and Karl Weierstraß .
↑ See Kreiser, p. 388 and Steinbach, p. 200.
↑ See W. Scharlau (Ed.): Mathematische Instituts in Deutschland, 1800–1945 , Vieweg, 1990
↑ See Kreiser, p. 478.
↑ See the article by Matthias Steinbach. Adolf Piltz's brother tried to keep the inheritance on his own. Piltz was accused of "indecent lifestyle" and alcoholism .
↑ See Steinbach, p. 207. As Ilmenau is about 100 kilometers from Bad Sulza, it is unclear whether he carried out both activities at the same time.
↑ Piltz's announcement appeared in Pfeiffer's work of 1884 ( About the periodicity in the divisibility of numbers and the distribution of the classes of positive quadratic forms on their determinants ) in a footnote. According to Landau, Ernst Pfeiffer had written this work under the guidance of Adolf Piltz.
↑ Even before that, works by Landau had the Piltz proof (and the possibility of simplifying it) on the topic, see e.g. B. On an ideal theoretical function , Trans. AMS 13 , 1-21, 1912.

personal data
SURNAME	Piltz, Adolf
BRIEF DESCRIPTION	German mathematician
DATE OF BIRTH	December 8, 1855
PLACE OF BIRTH	Ilmenau
DATE OF DEATH	1940
Place of death	with large herring

[1] And simultaneous doctorate supervised by Ernst Kummer and Karl Weierstraß .

[2] See Kreiser, p. 388 and Steinbach, p. 200.

[3] See W. Scharlau (Ed.): Mathematische Instituts in Deutschland, 1800–1945 , Vieweg, 1990

[4] See Kreiser, p. 478.

[5] See the article by Matthias Steinbach. Adolf Piltz's brother tried to keep the inheritance on his own. Piltz was accused of "indecent lifestyle" and alcoholism .

[6] See Steinbach, p. 207. As Ilmenau is about 100 kilometers from Bad Sulza, it is unclear whether he carried out both activities at the same time.

[7] Piltz's announcement appeared in Pfeiffer's work of 1884 ( About the periodicity in the divisibility of numbers and the distribution of the classes of positive quadratic forms on their determinants ) in a footnote. According to Landau, Ernst Pfeiffer had written this work under the guidance of Adolf Piltz.

[8] Even before that, works by Landau had the Piltz proof (and the possibility of simplifying it) on the topic, see e.g. B. On an ideal theoretical function , Trans. AMS 13 , 1-21, 1912.