On the Waring-Goldbach problem on average

2018/06/15 by Alessandro Languasco, Languasco, Alessandro
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1806.05861

openalex publication_date 2018/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let s, ℓ be two integers such that 2≤ s≤ ℓ-1, ℓ≥ 3. We prove that a suitable asymptotic formula for the average number of representations of integers n=∑_i=1^s p_i^ℓ, where p_i, i=1,\dotsc,s, are prime numbers, holds in short intervals.

Related

• The Average Number of Goldbach Representations
• Goldbach Representations with several primes
• Waring-Goldbach Problem with Piatetski-Shapiro Primes
• Average orders of Goldbach Estimates in Arithmetic Progressions
• Waring-Goldbach problem in short intervals