Arnold Walfisz

Arnold Walfisz
File:Walfisz,Arnold 1920 Göttingen.jpg 1920 at Göttingen
Born	(1892-07-02)2 July 1892 Warsaw, Congress Poland, Russian Empire
Died	Tbilisi, Georgia, Soviet Union
Nationality	Poland
Fields	Mathematics
Institutions	Tbilisi State University
Alma mater	University of Göttingen
Doctoral advisor	Edmund Landau
Doctoral students	Roza Gongadze Georgiy Lomadze Aleksandr Lursmanishvili
Known for	Siegel–Walfisz theorem

Arnold Walfisz (2 July 1892 – 29 May 1962) was a Polish mathematician working in analytic number theory.

Life

After the Abitur in Warsaw Arnold Walfisz studied (1909−14 and 1918−21) in Munich, Berlin, Heidelberg and Göttingen. Edmund Landau was his doctoral thesis supervisor at the University of Göttingen. Walfisz lived in Wiesbaden from 1922 through 1927, then he returned to Warsaw, worked at an insurance company and at the mathematical institute of the university (habilitation in 1930). In 1935, together with Salomon Lubelski, he founded the mathematical journal Acta Arithmetica. In 1936 Walfisz became professor at the University of Tbilisi in Georgia. He wrote approximately 100 mathematical articles and three books.

Work

By using a theorem by Carl Ludwig Siegel providing an upper bound for the real zeros (see Siegel zero) of Dirichlet L-functions formed with real non-principal characters, Walfisz obtained the Siegel-Walfisz theorem, from which the prime number theorem for arithmetic progressions can be deduced.

By using estimates on exponential sums due to I. M. Vinogradov and N. M. Korobov, Walfisz obtained the currently best O-estimates for the remainder terms of the summatory functions of both the sum-of-divisors function $\sigma$ and the Euler function $\phi$ (in: "Weylsche Exponentialsummen in der neueren Zahlentheorie", see below).

Works

• Pell's equation (in Russian), Tbilisi, 1952
• Gitterpunkte in mehrdimensionalen Kugeln, Panstwowe Wydawnictwo Naukowe, Monografi Matematyczne, vol. 33. Warszawa, 1957, online
• Weylsche Exponentialsummen in der neueren Zahlentheorie, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963

Further reading

• Ekkehard Krätzel, Christoph Lamm: Von Wiesbaden nach Tiflis – Die wechselvolle Lebensgeschichte des Zahlentheoretikers Arnold Walfisz (German), Mitteilungen der Deutschen Mathematiker-Vereinigung, Band 21 (1), 2013
• Sophie Goetzel-Leviathan (née Walfisz): Der Krieg von Innen (German), Paul Lazarus Stiftung, Wiesbaden, 2011

External links

• Short biography and list of works
• Biography from Acta Arithmetica, 1964
• Description of his work from Acta Arithmetica, 1964
• Arnold Walfisz at the Mathematics Genealogy Project