Arnold Walfisz
Arnold Walfisz was a Jewish-Polish mathematician working in analytic number theory.Life
After the Abitur in Warsaw, Arnold Walfisz studied 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. In 1935, together with, 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 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 , 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 .Works
- Pell's equation, Tbilisi, 1952
- Gitterpunkte in mehrdimensionalen Kugeln , Panstwowe Wydawnictwo Naukowe, Monografi Matematyczne, vol. 33. Warszawa, 1957,
- Weylsche Exponentialsummen in der neueren Zahlentheorie , VEB Deutscher Verlag der Wissenschaften, Berlin, 1963.
