Arnold Walfisz

Arnold Walfisz
1920 at Göttingen
Born 2 July 1892
Warsaw, Congress Poland, Russian Empire
Died 29 May 1962 (aged 69)
Tbilisi, Georgia, Soviet Union
Nationality  Poland
Fields Mathematics
Institutions Tbilisi State University
Alma mater University of Göttingen
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 (Poland), Arnold Walfisz studied (1909−14 and 1918−21) in Germany at 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 (pl), he founded the mathematical journal Acta Arithmetica. In 1936 Walfisz became professor at the University of Tbilisi in the nation of 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 (ru) , Walfisz obtained the currently best O-estimates for the remainder terms of the summatory functions of both the sum-of-divisors function ${\displaystyle \sigma }$ and the Euler function ${\displaystyle \phi }$ (in: "Weylsche Exponentialsummen in der neueren Zahlentheorie", see below).

Works

• Pell's equation (in Russian), Tbilisi, 1952
• Gitterpunkte in mehrdimensionalen Kugeln [Lattice points in multi-dimensional spheres], Panstwowe Wydawnictwo Naukowe, Monografi Matematyczne, vol. 33. Warszawa, 1957, online[1]
• Weylsche Exponentialsummen in der neueren Zahlentheorie [Weyl exponential sums in the newer number theory], VEB Deutscher Verlag der Wissenschaften, Berlin, 1963.