Results 21 to 30 of about 496 (82)
The quadratic Waring–Goldbach problem
Journal of Number Theory, 2004 The purpose of this paper is to show a new bound for the number \(E(N)\), say, of the natural numbers \(n\) such that \(n\leq N\), \(n\equiv4\pmod {24}\), and \(n\) cannot be written as the sum of four squares of primes. Actually, the authors establish the bound \(E(N)\ll N^{3/8+\varepsilon}\) with any fixed \(\varepsilon>0\). The proof is based on the
Liu, JY, Wooley, TD, Yu, G
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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
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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.
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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.
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On Waring–Goldbach problem of mixed powers
Journal de théorie des nombres de Bordeaux, 2017 Let P r denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper it is proved that for every sufficiently large odd integer N, the equationN=x2+p13+p23+p33+p43+p56+p67is solvable with x being an almost-prime P 42 and the other terms powers of primes.
Lü, Xiaodong, Mu, Quanwu
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Sum of one prime and two squares of primes in short intervals [PDF]
, 2015 Assuming the Riemann Hypothesis we prove that the interval $[N, N + H]$ contains an integer which is a sum of a prime and two squares of primes provided that $H \ge C (\log N)^{4}$, where $C > 0$ is an effective constant.Comment: removed unconditional ...
Languasco, Alessandro +1 more
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Linnik's approximation to Goldbach's conjecture, and other problems
, 2015 We examine the problem of writing every sufficiently large even number as the sum of two primes and at most $K$ powers of 2. We outline an approach that only just falls short of improving the current bounds on $K$.
Platt, Dave, Trudgian, Tim
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If You Prick Us: Masculinity and Circumcision Pain in the United States and Canada, 1960–2000
, 2020 Gender &History, Volume 32, Issue 1, Page 54-69, March 2020.
Laura M. Carpenter
wiley +1 more source
, 2015 Estimates are provided for $s$th moments of cubic smooth Weyl sums, when $4\le s\le 8$, by enhancing the author's iterative method that delivers estimates beyond classical convexity.
Wooley, Trevor D.
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Exceptional sets in Waring's problem: two squares and s biquadrates [PDF]
, 2014 Let $R_s(n)$ denote the number of representations of the positive number $n$ as the sum of two squares and $s$ biquadrates. When $s=3$ or $4$, it is established that the anticipated asymptotic formula for $R_s(n)$ holds for all $n\le X$ with at most $O(X^
Zhao, Lilu
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