Short intervals asymptotic formulae for binary problems with prime powers, II

Abstract

We improve some results about the asymptotic formulae in short intervals for the average number of representations of integers of the forms $n=p_1^{{\ell }_1}+p_2^{{\ell }_2}$ and $n=p^{{\ell }_1}+m^{{\ell }_2}$, where ${\ell }_1,{\ell }_2\ge 2$ are fixed integers, $p,p_1,p_2$ are prime numbers and $m$ is an integer.

arXiv comment16 pages

References in corpus (6)

• Sum of one prime and two squares of primes in short intervals
• On a ternary Diophantine problem with mixed powers of primes
• Short intervals asymptotic formulae for binary problems with primes and powers, II: density $1$
• Sums of four prime cubes in short intervals
• Short intervals asymptotic formulae for binary problems with primes and powers, I: density $3/2$
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Cited by in corpus (1)

• On an average ternary problem with prime powers