Noncommutative methods in additive combinatorics and number theory

2021 ◽  
Vol 76 (6) ◽  
Author(s):  
Ilya Dmitrievich Shkredov
Keyword(s):  
Number Theory ◽  
Additive Combinatorics

scholarly journals Integrality of hook ratios

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Paul-Olivier Dehaye
Keyword(s):  
Number Theory ◽  
Additional Condition ◽  
Complete Classification ◽  
Additive Combinatorics ◽  
Nous Obtenons ◽  
Analogous Question ◽  
International Audience ◽  
Cette Question

International audience We study integral ratios of hook products of quotient partitions. This question is motivated by an analogous question in number theory concerning integral factorial ratios. We prove an analogue of a theorem of Landau that already applied in the factorial case. Under the additional condition that the ratio has one more factor on the denominator than the numerator, we provide a complete classification. Ultimately this relies on Kneser's theorem in additive combinatorics. Nous étudions les fractions de produits d'équerres de partitions quotients. Cette question fait écho à une question en théorie des nombres sur les quotients entiers de factorielles. Nous prouvons un analogue du théorème de Landau, qui aidait déjà dans le cas des factorielles. Sous l'hypothèse supplémentaire d'une fraction avec un facteur de plus au dénominateur qu'au numérateur, nous obtenons une classification complète. Cette partie de la preuve repose sur un théorème de Kneser en combinatoire additive.

Multiplicative Number Theory I

2006 ◽  
Author(s):  
Hugh L. Montgomery ◽  
Robert C. Vaughan
Keyword(s):  
Number Theory

Mathematical proof that rocked number theory will be published

Nature ◽  
2020 ◽  
Vol 580 (7802) ◽  
pp. 177-177
Author(s):  
Davide Castelvecchi
Keyword(s):  
Number Theory ◽  
Mathematical Proof

Mathematics without Apologies

2017 ◽  
Author(s):  
Michael Harris
Keyword(s):  
Number Theory ◽  
Financial Crisis ◽  
Pop Culture ◽  
First Century ◽  
2008 Financial Crisis ◽  
Dinner Party ◽  
Mathematical Life ◽  
Personal Experiences ◽  
The 2008 Financial Crisis ◽  
Guided Tour

What do pure mathematicians do, and why do they do it? Looking beyond the conventional answers, this book offers an eclectic panorama of the lives and values and hopes and fears of mathematicians in the twenty-first century, assembling material from a startlingly diverse assortment of scholarly, journalistic, and pop culture sources. Drawing on the author's personal experiences as well as the thoughts and opinions of mathematicians from Archimedes and Omar Khayyám to such contemporary giants as Alexander Grothendieck and Robert Langlands, the book reveals the charisma and romance of mathematics as well as its darker side. In this portrait of mathematics as a community united around a set of common intellectual, ethical, and existential challenges, the book touches on a wide variety of questions, such as: Are mathematicians to blame for the 2008 financial crisis? How can we talk about the ideas we were born too soon to understand? And how should you react if you are asked to explain number theory at a dinner party? The book takes readers on an unapologetic guided tour of the mathematical life, from the philosophy and sociology of mathematics to its reflections in film and popular music, with detours through the mathematical and mystical traditions of Russia, India, medieval Islam, the Bronx, and beyond.

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