A Diophantine approximation problem with two primes and one k-th power of a prime

JOURNAL OF NUMBER THEORY

卷:188

Article

Gambini, Alessandro¹  Languasco, Alessandro²  Zaccagnini, Alessandro¹ 

[1] Univ Parma, Dipartimento Sci Matemat Fis & Informat, Parco Area Sci 53-a, I-43124 Parma, Italy

[2] Univ Padua, Dipartimento Matemat Tullio Levi Civita, Via Trieste 63, I-35121 Padua, Italy

关键词: Diophantine inequalities;    Goldbach-type problems;    Hardy Littlewood method;   

DOI  :  10.1016/j.jnt.2018.01.002

来源: Elsevier

【 摘 要 】

We refine a result of the last two Authors of [8] on a Diophantine approximation problem with two primes and a k-th power of a prime which was only proved to hold for 1 < k < 4/3. We improve the k-range to 1 < k <= 3 by combining Harman's technique on the minor arc with a suitable estimate for the L-4-norm of the relevant exponential sum over primes. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free