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Mathematics > Number Theory

arXiv:1812.08707 (math)
[Submitted on 20 Dec 2018 (v1), last revised 12 Dec 2019 (this version, v4)]

Title:Primos, paridad y análisis

Authors:Harald Helfgott, Adrián Ubis
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Abstract:Distinguir entre enteros con un número par o impar de divisores primos es una de las tareas más difíciles en la teoría analítica de números. Un trabajo reciente de Matomäki y Radziwiłł muestra que, en promedio, ambos existen con la misma frecuencia aún en intervalos muy cortos. Este avance ya ha tenido varias aplicaciones importantes en las manos de Matomäki, Radziwiłł, Tao y Teräväinen. Explicaremos en detalle una prueba completa del resultado original de Matomäki y Radziwiłł, así como de varias aplicaciones.
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To distinguish between integers with an even or an odd number of prime factors is one of the most difficult tasks in Analytic Number Theory. A recent work by Matomäki and Radziwiłł shows that, in average, both types of integers appear with the same frequency even in very short intervals. This breakthrough has already had several applications in the hands of Matomäki, Radziwiłł, Tao and Teräväinen. We explain in detail the complete proof of both the original result by Matomäki and Radziwiłł and of some of its applications.
Comments: 71 pages, in Spanish. Minor typos corrected
Subjects: Number Theory (math.NT)
Cite as: arXiv:1812.08707 [math.NT]
  (or arXiv:1812.08707v4 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1812.08707

Submission history

From: Adrián Ubis [view email]
[v1] Thu, 20 Dec 2018 17:16:39 UTC (72 KB)
[v2] Wed, 27 Mar 2019 17:21:38 UTC (73 KB)
[v3] Fri, 7 Jun 2019 10:44:57 UTC (73 KB)
[v4] Thu, 12 Dec 2019 21:10:55 UTC (73 KB)
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