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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2019, Volume 106, Issue 1, Pages 95–107 (Mi mz12178)

On the Partition of an Odd Number into Three Primes in a Prescribed Proportion

A. A. Sagdeev

Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region

Abstract: We prove that, for any partition $1=a+b+c$ of unity into three positive summands, each odd number $n$ can be subdivided into three primes $n=p_a(n)+p_b(n)+p_c(n)$ so that the fraction of the first summand will approach $a$, that of the second, $b$, and that of the third, $c$ as $n \to \infty$.

Keywords: Goldbach–Vinogradov theorem, distribution of primes, Hardy–Littlewood circle method, trigonometric sums.

 Funding Agency Grant Number Russian Foundation for Basic Research 18-01-00355 Ministry of Education and Science of the Russian Federation ÍØ-6760.2018.1 Simons Foundation This work was supported in part by the Russian Foundation for Basic Research under grant 18-01-00355, by the program “Leading Scientific Schools” under grant NSh-6760.2018.1, and by the Simons Foundation.

DOI: https://doi.org/10.4213/mzm12178

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English version:
Mathematical Notes, 2019, 106:1, 98–107

Bibliographic databases:

UDC: 511.3
Revised: 30.10.2018

Citation: A. A. Sagdeev, “On the Partition of an Odd Number into Three Primes in a Prescribed Proportion”, Mat. Zametki, 106:1 (2019), 95–107; Math. Notes, 106:1 (2019), 98–107

Citation in format AMSBIB
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