Arnold Walfisz

Arnold Walfisz
Arnold Walfisz
	1920 at Göttingen
Born	2 July 1892; Warsaw, Congress Poland, Russian Empire
Died	29 May 1962 (aged 69); Tbilisi, Georgian SSR, Soviet Union
Nationality	Poland
Alma mater	University of Göttingen
Known for	Siegel–Walfisz theorem
	Scientific career
Fields	Mathematics
Institutions	Tbilisi State University
Doctoral advisor	Edmund Landau

Arnold Walfisz (2 July 1892 – 29 May 1962) was a Jewish-Polish^[1] 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 Soviet 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 $\sigma$ 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 [Lattice points in multi-dimensional spheres], Panstwowe Wydawnictwo Naukowe, Monografi Matematyczne, vol. 33. Warszawa, 1957, online^[2]
Weylsche Exponentialsummen in der neueren Zahlentheorie [Weyl exponential sums in the newer number theory], VEB Deutscher Verlag der Wissenschaften, Berlin, 1963.

References

^ O'Connor, John J.; Robertson, Edmund F., "Arnold Walfisz", MacTutor History of Mathematics Archive, University of St Andrews
^ Chowla, S. (1959). "Review: A. Walfisz, Gitterpunkte in mehrdimensionalen Kugeln" [Lattice points in multi-dimensional spheres]. Bull. Amer. Math. Soc. 65 (1): 23–25. doi:10.1090/S0002-9904-1959-10265-2.

External links

[1] O'Connor, John J.; Robertson, Edmund F., "Arnold Walfisz", MacTutor History of Mathematics Archive, University of St Andrews

[2] Chowla, S. (1959). "Review: A. Walfisz, Gitterpunkte in mehrdimensionalen Kugeln" [Lattice points in multi-dimensional spheres]. Bull. Amer. Math. Soc. 65 (1): 23–25. doi:10.1090/S0002-9904-1959-10265-2.

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