Asymptotic formula for the sum of a prime and a square-full number in short intervals

2024/05/07 by Fumi Ogihara, Yuta Suzuki, Ogihara, Fumi +1 · 1 citation
Mathematics · #11P32 #Advanced Mathematical Theories #Algebraic and Geometric Analysis #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2405.04509

openalex publication_date 2024/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let R_{m, sq-full}(N) be a representation function for the sum of a prime and a square-full number. In this article, we prove an asymptotic formula for the sum of R_{m, sq-full}(N) over positive integers N in a short interval (X, X+H] of length H slightly bigger than X^(1)/(2).

Cited by

• Asymptotic formula for the sum of a prime and a square-full number in short intervals shorter than X^1/2

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