Results 11 to 20 of about 270 (42)
AN $L$ -FUNCTION-FREE PROOF OF VINOGRADOV’S THREE PRIMES THEOREM
Forum of Mathematics, Sigma, 2014 We give a new proof of Vinogradov’s three primes theorem, which asserts that all sufficiently large odd positive integers can be written as the sum of three primes. Existing proofs rely on the theory of
XUANCHENG SHAO
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A Ces\`aro Average of Goldbach numbers [PDF]
, 2012 Let $\Lambda$ be the von Mangoldt function and $(r_G(n) = \sum_{m_1 + m_2 = n} \Lambda(m_1) \Lambda(m_2))$ be the counting function for the Goldbach numbers. Let $N \geq 2$ be an integer.
Languasco, Alessandro +1 more
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Quantitative relations between short intervals and exceptional sets of cubic Waring-Goldbach problem
Open Mathematics, 2017 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 ...
Feng Zhao
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PRIME SOLUTIONS TO POLYNOMIAL EQUATIONS IN MANY VARIABLES AND DIFFERING DEGREES
Forum of Mathematics, Sigma, 2018 Let $\mathbf{f}=(f_{1},\ldots ,f_{R})$ be a system of polynomials with integer coefficients in which the degrees need not all be the same. We provide sufficient conditions for which the system of equations $f_{j}(x_{1},\ldots ,x_{n})=0~(1\leqslant j ...
SHUNTARO YAMAGISHI
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On Diophantine approximation by unlike powers of primes
Open Mathematics, 2019 Suppose that λ1, λ2, λ3, λ4, λ5 are nonzero real numbers, not all of the same sign, λ1/λ2 is irrational, λ2/λ4 and λ3/λ5 are rational. Let η real, and ε > 0.
Ge Wenxu, Li Weiping, Wang Tianze
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On the Waring--Goldbach problem for eighth and higher powers [PDF]
, 2015 Recent progress on Vinogradov's mean value theorem has resulted in improved estimates for exponential sums of Weyl type. We apply these new estimates to obtain sharper bounds for the function $H(k)$ in the Waring--Goldbach problem.
Angel V. Kumchev, D. Wooley, Trevor
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The jumping champion conjecture [PDF]
, 2012 An integer $d$ is called a jumping champion for a given $x$ if $d$ is the most common gap between consecutive primes up to $x$. Occasionally several gaps are equally common. Hence, there can be more than one jumping champion for the same $x$.
Andrew H. Ledoan +5 more
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, 2008 We show a smoothed version of Goldston-Pintz-Yildirim's sifting argument to detect small gaps between primes, which has a higly flexible error term. Our argument is applicable to high dimensional Selberg sieve situations as well, although the relevant ...
Motohashi, Yoichi, Pintz, Janos
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Dynamical Sieve of Eratosthenes
, 2011 In this document, prime numbers are related as functions over time, mimicking the Sieve of Eratosthenes. For this purpose, the mathematical representation is a uni-dimentional time line depicting the number line for positive natural numbers N, where each
Mateos, Luis A.
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A Diophantine approximation problem with two primes and one k-power of a prime [PDF]
, 2018 We refine a result of the last two Authors on a Diophantine approximation problem with two primes and a k-th power of a prime which was only proved to hold for ...
Alessandro, Gambini +2 more
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