1920 at Göttingen
2 July 1892|
Warsaw, Congress Poland, Russian Empire
|Died||29 May 1962
Tbilisi, Georgia, Soviet Union
|Institutions||Tbilisi State University|
|Alma mater||University of Göttingen|
|Doctoral advisor||Edmund Landau|
|Doctoral students||Roza Gongadze
|Known for||Siegel–Walfisz theorem|
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.
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 and the Euler function (in: "Weylsche Exponentialsummen in der neueren Zahlentheorie", see below).
- 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
- Chowla, S. (1959). "Review: A. Walfisz, Gitterpunkte in mehrdimensionalen Kugeln". Bull. Amer. Math. Soc. 65 (1): 23–25.
- 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