Results 21 to 30 of about 126,211 (116)
Exceptional Sets for Sums of Prime Cubes in Short Interval
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 Let E(N, X) denote the number of even integers n, with N − X ≤ n ≤ N, such that n cannot be written as n=p13+⋯+p83. We prove that if X > N1/36+ɛ, then E(N, X) = o(X).
Gongrui Chen, Jie Wu
wiley +1 more source
On the Hybrid Power Mean of Two‐Term Exponential Sums and Cubic Gauss Sums
Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 In this paper, an interesting third‐order linear recurrence formula is presented by using elementary and analytic methods. This formula is concerned with the calculating problem of the hybrid power mean of a certain two‐term exponential sums and the cubic Gauss sums.
Shaofan Cao +2 more
wiley +1 more source
ON THE WARING–GOLDBACH PROBLEM FOR CUBES [PDF]
Glasgow Mathematical Journal, 2009 AbstractWe prove that almost all natural numbers satisfying certain necessary congruence conditions can be written as the sum of two cubes of primes and two cubes of P2-numbers, where, as usual, we call a natural number a P2-number when it is a prime or the product of two primes. From this result we also deduce that every sufficiently large integer can
Brüdern, Jörg, Kawada, Koichi
openaire +3 more sources
On the Waring-Goldbach Problem for One Square and Five Cubes in Short Intervals [PDF]
Czechoslovak Mathematical Journal, 2020 Let N be a sufficiently large integer. We prove that almost all sufficiently large even integers n ∈ [ N − 6 U, N + 6 U ] can be represented as $$\left\{ {\matrix{ {n = p_1^2 + p_2^3 + p_3^3 + p_4^3 + p_5^3 + p_6^3} \hfill \cr {\left| {p_1^2 - {N \over 6}
Fei Xue, Min Zhang, Jinjia Li
semanticscholar +2 more sources
On Waring–Goldbach problem with Piatetski-Shapiro primes [PDF]
Journal of Number Theory, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Akbal, Yıldırım, Güloğlu, Ahmet M.
openaire +4 more sources
Waring-Goldbach Problem with Piatetski-Shapiro Primes [PDF]
, 2016 In this paper, we exhibit an asymptotic formula for the number of representations of a large integer as a sum of a fixed power of Piatetski-Shapiro primes, thereby establishing a variant of Waring-Goldbach problem with primes from a sparse sequence.
Yildirim Akbal, A. M. Guloglu
semanticscholar +1 more source
Short intervals asymptotic formulae for binary problems with primes and powers, I: density 3/2 [PDF]
, 2016 We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime and a square, or a prime square.
A., Zaccagnini, Languasco, Alessandro
core +4 more sources
On Sums of Powers of Almost Equal Primes [PDF]
, 2014 We investigate the Waring-Goldbach problem of representing a positive integer $n$ as the sum of $s$ $k$th powers of almost equal prime numbers. Define $s_k=2k(k-1)$ when $k\ge 3$, and put $s_2=6$.
Wei, Bin, Wooley, Trevor D.
core +5 more sources
Relations between exceptional sets for additive problems [PDF]
, 2010 We describe a method for bounding the set of exceptional integers not represented by a given additive form in terms of the exceptional set corresponding to a subform. Illustrating our ideas with examples stemming from Waring's problem for cubes, we show,
Kawada, Koichi, Wooley, Trevor D.
core +3 more sources
EXPONENTIAL SUMS OVER PRIMES IN SHORT INTERVALS AND AN APPLICATION TO THE WARING–GOLDBACH PROBLEM [PDF]
Mathematika, 2014 Let $\Lambda(n)$ be the von Mangoldt function, $x$ real and $2\leq y \leq x$. This paper improves the estimate on the exponential sum over primes in short intervals \[ S_k(x,y;\alpha) = \sum_{x< n \leq x+y} \Lambda(n) e\left( n^k \alpha \right) \] when $
Bingrong Huang
semanticscholar +1 more source