Short intervals asymptotic formulae for binary problems with primes and powers, II: density $1$

Abstract

We prove that suitable asymptotic formulae in short intervals hold for the problems of representing an integer as a sum of a prime square and a square, or a prime square. Such results are obtained both assuming the Riemann Hypothesis and in the unconditional case.

revised version

References in corpus (2)

• Sum of one prime and two squares of primes in short intervals
• Short intervals asymptotic formulae for binary problems with primes and powers, I: density $3/2$

Cited by in corpus (6)

• Sums of four prime cubes in short intervals
• Short intervals asymptotic formulae for binary problems with prime powers
• Short intervals asymptotic formulae for binary problems with primes and powers, I: density $3/2$
• Short intervals asymptotic formulae for binary problems with prime powers, II
• On the average number of representations of an integer as a sum of polynomials computed at prime values
• On an average ternary problem with prime powers