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| {{Infobox scientist
| | The author is [https://Www.Costcoauto.com/vpp/about.aspx called Araceli] Gulledge. The factor I adore most bottle tops collecting and now I have time to take on new things. My job is a production and distribution officer and [http://www.wikihow.com/Buy-an-Extended-Warranty-for-a-Car I'm performing] pretty good financially. [http://enjoythisworld.com/UserProfile/tabid/464/userId/33651/Default.aspx extended auto warranty] warranty Alabama is [http://jamsuham.net/xe/joinqna/670399 extended car warranty] auto warranty where he and his [http://Www.Popularmechanics.com/cars/how-to/repair/how-to-get-a-used-car-warranty-and-not-get-screwed-6654348 spouse live] car auto warranty warranty and he has every thing that he requirements there.<br><br>Here is my web site ... [http://www.Thehubermangroup.com/ActivityFeed/MyProfile/tabid/60/userId/24292/Default.aspx extended auto warranty] |
| | name = Arnold Walfisz
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| | image = Walfisz,Arnold 1920 Göttingen.jpg
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| | image_size =
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| | caption = 1920 at Göttingen
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| | birth_date = {{birth date|1892|07|02|df=y}}
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| | birth_place = [[Warsaw]], [[Congress Poland]], [[Russian Empire]]
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| | death_date = {{death date and age|1962|05|29|1892|07|02|df=y}}
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| | death_place = [[Tbilisi]], [[Georgian Soviet Socialist Republic|Georgia]], [[Soviet Union]]
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| | nationality = {{flag|Poland}}
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| | fields = [[Mathematics]]
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| | workplaces = [[Tbilisi State University]]
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| | alma_mater = [[University of Göttingen]]
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| | doctoral_advisor = [[Edmund Landau]]
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| | doctoral_students = [[Roza Gongadze]]<br>[[Georgiy Lomadze]]<br>[[Aleksandr Lursmanishvili]]
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| | known_for = [[Siegel–Walfisz theorem]]
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| | awards =
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| }}
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| '''Arnold Walfisz''' (2 July 1892 – 29 May 1962) was a [[Poles|Polish]] [[mathematician]] working in [[analytic number theory]].
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| == Life ==
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| After the ''[[Abitur]]'' in Warsaw Arnold Walfisz studied (1909−14 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 [[Tbilisi State University|University of Tbilisi]] in [[Georgia (country)|Georgia]]. He wrote approximately 100 mathematical articles and three books.
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| == Work ==
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| By using a theorem by [[Carl Ludwig Siegel]] providing an upper bound for the real zeros (see [[Siegel zero]]) of [[Dirichlet L-function]]s formed with real non-principal characters, Walfisz obtained the [[Siegel-Walfisz theorem]], from which the [[Prime number theorem#Prime number theorem for arithmetic progressions|prime number theorem for arithmetic progressions]] can be deduced.
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| By using estimates on exponential sums due to [[Ivan Matveyevich Vinogradov|I. M. Vinogradov]] and [[N. M. Korobov]], Walfisz obtained the currently best [[Big O notation|O-estimates]] for the remainder terms of the summatory functions of both the sum-of-divisors function <math>\sigma</math> and the Euler function <math>\phi</math> (in: "Weylsche Exponentialsummen in der neueren Zahlentheorie", see below).
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| ==Works==
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| *''Pell's equation'' (in Russian), Tbilisi, 1952
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| *''Gitterpunkte in mehrdimensionalen Kugeln'', Panstwowe Wydawnictwo Naukowe, Monografi Matematyczne, vol. 33. Warszawa, 1957, [http://matwbn.icm.edu.pl/kstresc.php?tom=33&wyd=10 online]<ref>{{cite journal|author=Chowla, S.|title=Review: A. Walfisz, ''Gitterpunkte in mehrdimensionalen Kugeln''|journal=Bull. Amer. Math. Soc.|year=1959|volume=1959|volume=65|issue=1|pages=23–25|url=http://projecteuclid.org/euclid.bams/1183523000}}</ref>
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| *''Weylsche Exponentialsummen in der neueren Zahlentheorie'', VEB Deutscher Verlag der Wissenschaften, Berlin, 1963
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| ==References==
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| {{reflist}}
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| == External links ==
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| *[http://www.rmi.ge/person/walfisz/ Short biography and list of works]
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| *[http://matwbn.icm.edu.pl/ksiazki/aa/aa10/aa10110.pdf Biography from ''Acta Arithmetica'', 1964]
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| *[http://matwbn.icm.edu.pl/ksiazki/aa/aa10/aa10111.pdf Description of his work from ''Acta Arithmetica'', 1964]
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| *{{MathGenealogy |id=65517 }}
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| {{Authority control|VIAF=3255823}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Walfisz, Arnold
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = Polish mathematician
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| | DATE OF BIRTH = 2 July 1892
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| | PLACE OF BIRTH = [[Warsaw]], [[Congress Poland]], [[Russian Empire]]
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| | DATE OF DEATH = 29 May 1962
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| | PLACE OF DEATH = [[Tbilisi]], [[Georgian Soviet Socialist Republic|Georgia]], [[Soviet Union]]
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| }}
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| {{DEFAULTSORT:Walfisz, Arnold}}
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| [[Category:1892 births]]
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| [[Category:1962 deaths]]
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| [[Category:Number theorists]]
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| [[Category:Polish mathematicians]]
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| [[Category:People from Warsaw]]
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