Results 51 to 60 of about 126,211 (116)
Sums of two squares and a power
, 2016 We extend results of Jagy and Kaplansky and the present authors and show that for all $k\geq 3$ there are infinitely many positive integers $n$, which cannot be written as $x^2+y^2+z^k=n$ for positive integers $x,y,z$, where for $k\not\equiv 0 \bmod 4$ a
C. Hooley +10 more
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A Waring–Goldbach type problem for mixed powers
Journal of Number Theory, 2014 Let \(R_4(N)\) denote the number of ways of writing \(N\) in the form \[ N=x^2+p_2^2+p_3^3+p_4^4+p_5^4+p_6^4, \] where \(p_j\)'s are primes and \(x\) is a \(P_6\) (a \(P_r\) means an integer having at most \(r\) prime factors, counted according to multiplicity).
openaire +2 more sources
Mean values of Dirichlet polynomials and applications to linear equations with prime variables
, 2004 We prove a new mean-value theorem for Dirichlet polynomials with coefficients given by the von Mangoldt function. We then use our theorem to derive new estimates for certain exponential sums over primes.
Angel V. Kumchev +2 more
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Applications of some exponential sums on prime powers: a survey
, 2016 A survey paper on some recent results on additive problems with prime ...
Languasco, Alessandro
core
Some results on Waring-Goldbach type problems
, 2015 This thesis consists of three topics. The first one is on quadratic Waring-Goldbach problems. The second topic is about some additive problems involving fourth powers. The last topic is to consider an average result for the divisor problem in arithmetic progressions. Chapter 1 is an introduction.
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On the Waring-Goldbach problem on average
, 2018 Let $s$, $\ell$ be two integers such that $2\le s\le \ell-1$, $\ell\ge 3$. We prove that a suitable asymptotic formula for the average number of representations of integers $n=\sum_{i=1}^{s} p_{i}^{\ell}$, where $p_i$, $i=1,\dotsc,s$, are prime numbers, holds in short intervals.
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Cubic Waring-Goldbach problem with Piatetski-Shapiro primes
In this paper, it is proved that, for $γ\in(\frac{317}{320},1)$, every sufficiently large odd integer can be written as the sum of nine cubes of primes, each of which is of the form $[n^{1/γ}]$. This result constitutes an improvement upon the previous result of Akbal and Güloğlu [1].
Long, Linji +3 more
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On the Waring-Goldbach Problem for tenth powers
, 2016 Using sharper Weyl sum estimates, we show that $H(10)\le 105$, improving upon the previous bound of $107$.
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On the Waring–Goldbach Problem for Fourth and Fifth Powers
, 2001 K. Kawada, T. Wooley
semanticscholar +1 more source