Arnold Walfisz (2 July 1892 – 29 May 1962) was a Jewish-Polish

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

working in

analytic number theory In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers. It is often said to have begun with Peter Gustav Lejeune Dirichlet's 1837 introduction of Diric ...

Life

After the ''

Abitur ''Abitur'' (), often shortened colloquially to ''Abi'', is a qualification granted at the end of secondary education in Germany. It is conferred on students who pass their final exams at the end of ISCED 3, usually after twelve or thirteen year ...

'' in Warsaw (Poland), Arnold Walfisz studied (1909−14 and 1918−21) in Germany at

Munich Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the States of Germany, German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the List of cities in Germany by popu ...

Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...

Heidelberg Heidelberg (; Palatine German language, Palatine German: ''Heidlberg'') is a city in the States of Germany, German state of Baden-Württemberg, situated on the river Neckar in south-west Germany. As of the 2016 census, its population was 159,914 ...

and

Göttingen Göttingen (, , ; nds, Chöttingen) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. At the end of 2019, t ...

Edmund Landau Edmund Georg Hermann Landau (14 February 1877 – 19 February 1938) was a German mathematician who worked in the fields of number theory and complex analysis. Biography Edmund Landau was born to a Jewish family in Berlin. His father was Leopold ...

was his doctoral-thesis supervisor at the

University of Göttingen The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...

. Walfisz lived in

Wiesbaden Wiesbaden () is a city in central western Germany and the capital of the state of Hesse. , it had 290,955 inhabitants, plus approximately 21,000 United States citizens (mostly associated with the United States Army). The Wiesbaden urban area ...

from 1922 through 1927, then he returned to Warsaw, worked at an insurance company and at the mathematical institute of the university (

habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...

in 1930). In 1935, together with , he founded the mathematical journal ''

Acta Arithmetica ''Acta Arithmetica'' is a scientific journal of mathematics publishing papers on number theory. It was established in 1935 by Salomon Lubelski and Arnold Walfisz. The journal is published by the Institute of Mathematics of the Polish Academy of Sc ...

''. In 1936, Walfisz became professor at the University of Tbilisi in the nation of

Georgia Georgia most commonly refers to: * Georgia (country), a country in the Caucasus region of Eurasia * Georgia (U.S. state), a state in the Southeast United States Georgia may also refer to: Places Historical states and entities * Related to the ...

(at the time a part of the

Soviet Union The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen national ...

). He wrote approximately 100 mathematical articles and three books.

Work

By using a theorem by

Carl Ludwig Siegel Carl Ludwig Siegel (31 December 1896 – 4 April 1981) was a German mathematician specialising in analytic number theory. He is known for, amongst other things, his contributions to the Thue–Siegel–Roth theorem in Diophantine approximation, ...

providing an upper bound for the real zeros (see

Siegel zero Siegel (also Segal or Segel), is a German and Ashkenazi Jewish surname. it can be traced to 11th century Bavaria and was used by people who made wax seals for or sealed official documents (each such male being described as a ''Siegelbeamter''). A ...

) of

Dirichlet L-function In mathematics, a Dirichlet ''L''-series is a function of the form :L(s,\chi) = \sum_^\infty \frac. where \chi is a Dirichlet character and ''s'' a complex variable with real part greater than 1. It is a special case of a Dirichlet series. By a ...

s formed with real non-principal characters, Walfisz obtained the

Siegel–Walfisz theorem In analytic number theory, the Siegel–Walfisz theorem was obtained by Arnold Walfisz as an application of a theorem by Carl Ludwig Siegel to primes in arithmetic progressions. It is a refinement both of the prime number theorem and of Dirichlet's ...

, from which the

prime number theorem for arithmetic progressions In mathematics, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers. It formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying t ...

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

\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'' attice points in multi-dimensional spheres Panstwowe Wydawnictwo Naukowe, Monografi Matematyczne, vol. 33. Warszawa, 1957
online
ref> *''Weylsche Exponentialsummen in der neueren Zahlentheorie'' eyl exponential sums in the newer number theory

VEB Deutscher Verlag der Wissenschaften (DVW) (English: ''German Publisher of Sciences'') was a scientific publishing house in the former German Democratic Republic (GDR/). Situated in Berlin, DVW was founded as (VEB) on 1 January 1954 as the successor of the main department of "un ...

, Berlin, 1963.

References

External links

Short biography and list of worksBiography from ''Acta Arithmetica'', 1964Description of his work from ''Acta Arithmetica'', 1964
* {{DEFAULTSORT:Walfisz, Arnold 1892 births 1962 deaths 19th-century Polish Jews Number theorists 20th-century Polish mathematicians Scientists from Warsaw Academic staff of Tbilisi State University Polish emigrants to the Soviet Union

Life

Work

Works

Further reading

References

External links