Waring-Goldbach problem in short intervals

2019/12/04 by Wang, Mengdi
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1912.02310

Abstract

Let k≥2 and s be positive integers. Let θ∈(0,1) be a real number. In this paper, we establish that if s>k(k+1) and θ>0.55, then every sufficiently large natural number n, subjects to certain congruence conditions, can be written as n=p₁^k+⋯+p_s^k, where p_i(1≤ i≤ s) are primes in the interval (((n)/(s))^(1)/(k)-n^\fracθk,((n)/(s))^(1)/(k)+n^\fracθk]. The second result of this paper is to show that if s>(k(k+1))/(2) and θ>0.55, then almost all integers n, subject to certain congruence conditions, have above representation.

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