Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem

• Autorzy: Zhao Feng
• Języki publikacji: EN

Abstrakty

EN

In this paper, we are able to prove that almost all integers n satisfying some necessary congruence conditions are the sum of j almost equal prime cubes with j = 7, 8, i.e., [...] N=p13+…+pj3 $\begin{array}{} N=p_1^3+ \ldots +p_j^3 \end{array} $ with [...] |pi−(N/j)1/3|≤N1/3−δ+ε(1≤i≤j), $\begin{array}{} |p_i-(N/j)^{1/3}|\leq N^{1/3- \delta +\varepsilon} (1\leq i\leq j), \end{array} $ for some [...] 0<δ≤190. $\begin{array}{} 0 \lt \delta\leq\frac{1}{90}. \end{array} $ Furthermore, we give the quantitative relations between the length of short intervals and the size of exceptional sets.

Słowa kluczowe

EN

Circle method; Exponential sums over primes; Short intervals; Quantitative relations

Kategorie tematyczne

• 11N36: Applications of sieve methods
• 11P32: Goldbach-type theorems; other additive questions involving primes
• 11P05: Waring's problem and variants
• 11P55: Applications of the Hardy-Littlewood method

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 1517-1529

Daty

wydano

2017-01-01

otrzymano

2016-07-28

zaakceptowano

2017-11-14

online

2017-12-29

Twórcy

autor

Zhao Feng

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Identyfikatory

DOI

10.1515/math-2017-0130