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Start Over Descriptor "exponential sums over primes" Publisher de gruyter
2 results on '"exponential sums over primes"'

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

Author

Feng Zhao

Subjects
circle method, exponential sums over primes, short intervals, quantitative relations, 11p32, 11p05, 11n36, 11p55, Mathematics, QA1-939
Abstract

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

Published
2017
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2. Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem

Author

Zhao Feng

Subjects
General Mathematics, 010102 general mathematics, 0102 computer and information sciences, 01 natural sciences, circle method, Combinatorics, 11n36, short intervals, 010201 computation theory & mathematics, quantitative relations, 11p05, Waring–Goldbach problem, exponential sums over primes, QA1-939, 0101 mathematics, 11p32, Mathematics, 11p55
Abstract

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., $\begin{array}{} N=p_1^3+ \ldots +p_j^3 \end{array} $ with $\begin{array}{} |p_i-(N/j)^{1/3}|\leq N^{1/3- \delta +\varepsilon} (1\leq i\leq j), \end{array} $ for some $\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.

Published
2017

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