Partitions into three generalized D. H. Lehmer numbers

Mingxuan Zhong; Tianping Zhang; Mingxuan Zhong; Tianping Zhang

doi:10.3934/math.2024196

AIMS Mathematics

2024, Volume 9, Issue 2: 4021-4031. doi: 10.3934/math.2024196

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Partitions into three generalized D. H. Lehmer numbers

Mingxuan Zhong ¹,
Tianping Zhang ^{1,2
,
,}

1.
School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, Shaanxi, China
2.
Research Center for Number Theory and Its Applications, Northwest University, Xi'an 710127, Shaanxi, China

Received: 14 September 2023 Revised: 19 November 2023 Accepted: 29 November 2023 Published: 12 January 2024
MSC : 11P55, 11L05

In this paper, we derived that a sufficiently large integer $ N $ can always be represented as the sum of three generalized D. H. Lehmer numbers. As a consequence, we deduced Lu and Yi's original result (Monatsh. Math., 159 (2010), 45–58).
- D. H. Lehmer number,
- circle method,
- exponential sums,
- Bombieri-Weil bound
Citation: Mingxuan Zhong, Tianping Zhang. Partitions into three generalized D. H. Lehmer numbers[J]. AIMS Mathematics, 2024, 9(2): 4021-4031. doi: 10.3934/math.2024196

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Abstract

In this paper, we derived that a sufficiently large integer $ N $ can always be represented as the sum of three generalized D. H. Lehmer numbers. As a consequence, we deduced Lu and Yi's original result (Monatsh. Math., 159 (2010), 45–58).

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