Arnold Walfisz
Encyclopedia
Arnold Walfisz was a Polish
mathematician
working in analytic number theory
.
in Warsaw Arnold Walfisz studied (1910−14 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.
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.
Poles
thumb|right|180px|The state flag of [[Poland]] as used by Polish government and diplomatic authoritiesThe Polish people, or Poles , are a nation indigenous to Poland. They are united by the Polish language, which belongs to the historical Lechitic subgroup of West Slavic languages of Central Europe...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
working in analytic number theory
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 Dirichlet's introduction of Dirichlet L-functions to give the first proof of Dirichlet's theorem on arithmetic...
.
Life
After the AbiturAbitur
Abitur is a designation used in Germany, Finland and Estonia for final exams that pupils take at the end of their secondary education, usually after 12 or 13 years of schooling, see also for Germany Abitur after twelve years.The Zeugnis der Allgemeinen Hochschulreife, often referred to as...
in Warsaw Arnold Walfisz studied (1910−14 and 1918−21) in Munich
Munich
Munich The city's motto is "" . Before 2006, it was "Weltstadt mit Herz" . Its native name, , is derived from the Old High German Munichen, meaning "by the monks' place". The city's name derives from the monks of the Benedictine order who founded the city; hence the monk depicted on the city's coat...
, Berlin
Berlin
Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...
, Heidelberg
Heidelberg
-Early history:Between 600,000 and 200,000 years ago, "Heidelberg Man" died at nearby Mauer. His jaw bone was discovered in 1907; with scientific dating, his remains were determined to be the earliest evidence of human life in Europe. In the 5th century BC, a Celtic fortress of refuge and place of...
and Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
. Edmund Landau
Edmund Landau
Edmund Georg Hermann Landau was a German Jewish mathematician who worked in the fields of number theory and complex analysis.-Biography:...
was his doctoral thesis supervisor at the University of Göttingen. Walfisz lived in Wiesbaden
Wiesbaden
Wiesbaden is a city in southwest Germany and the capital of the federal state of Hesse. It has about 275,400 inhabitants, plus approximately 10,000 United States citizens...
from 1922 through 1927, then he returned to Warsaw, worked at an insurance company and at the mathematical institute of the university (habilitation
Habilitation
Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a PhD, habilitation requires the candidate to write a professorial thesis based on independent...
in 1930). In 1935, together with Salomon Lubelski, he founded the mathematical journal Acta Arithmetica
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 Sciences....
. In 1936 Walfisz became professor at the University of Tbilisi
Tbilisi State University
Ivane Javakhishvili Tbilisi State University , better known as Tbilisi State University , is a university established on 8 February 1918 in Tbilisi, Georgia. TSU is the oldest university in the whole Caucasus region...
in Georgia
Georgia (country)
Georgia is a sovereign state in the Caucasus region of Eurasia. Located at the crossroads of Western Asia and Eastern Europe, it is bounded to the west by the Black Sea, to the north by Russia, to the southwest by Turkey, to the south by Armenia, and to the southeast by Azerbaijan. The capital of...
. He wrote approximately 100 mathematical articles and three books.
Work
By using a theorem by Carl Ludwig SiegelCarl Ludwig Siegel
Carl Ludwig Siegel was a mathematician specialising in number theory and celestial mechanics. He was one of the most important mathematicians of the 20th century.-Biography:...
providing an upper bound for the real zeros (see Siegel zero
Siegel zero
In mathematics, more specifically in the field of analytic number theory, a Siegel zero, named after Carl Ludwig Siegel, is a type of potential counterexample to the generalized Riemann hypothesis, on the zeroes of Dirichlet L-function....
) of Dirichlet L-functions formed with real non-principal characters, Walfisz obtained the Siegel-Walfisz theorem
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.-Statement of the Siegel–Walfisz theorem:Define...
, from which the prime number theorem for arithmetic progressions can be deduced.
Works
- 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