Sums of four prime cubes in short intervals

Abstract

We prove that a suitable asymptotic formula for the average number of representations of integers $n=p_1^3+p_2^3+p_3^3+p_4^3$, where $p_1,p_2,p_3,p_4$ are prime numbers, holds in intervals shorter than the the ones previously known.

Unconditional result improved by using a Robert-Sargos estimate (lemmas 6-7); more detailed proof of Lemma 5 inserted. Correction of a typo. 10 pages

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, II: density $1$

Cited by in corpus (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