TITLE

# On the sum of a prime and a k-th power of prime in short intervals

AUTHOR(S)
Wang, Y.
PUB. DATE
May 2012
SOURCE
Acta Mathematica Hungarica;May2012, Vol. 135 Issue 3, p248
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
Let $\mathcal{H}_{k}$ denote the set { nâˆ£2| n, $n\not\equiv 1\ (\mathrm{mod}\ p)$ âˆ€ p>2 with pâˆ’1| k}. We prove that when $X^{\frac{11}{20}\left(1-\frac{1}{2k}\right) +\varepsilon}\leqq H\leqq X$, almost all integers $n\in\allowbreak {\mathcal{H}_{k} \cap (X, X+H]}$ can be represented as the sum of a prime and a k-th power of prime for kâ‰§3. Moreover, when $X^{\frac{11}{20}\left(1-\frac{1}{k}\right) +\varepsilon}\leqq H\leqq X$, almost all integers nâˆˆ( X, X+ H] can be represented as the sum of a prime and a k-th power of integer for kâ‰§3.
ACCESSION #
73983388

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