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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Bounds for prime solutions of some diagonal equations. II


Author: Ming Chit Liu
Journal: Trans. Amer. Math. Soc. 297 (1986), 415-426
MSC: Primary 11D41; Secondary 11P55
MathSciNet review: 854075
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Abstract: Let $ {b_j}$ and $ m$ be certain integers. In this paper we obtain a bound for prime solutions $ {p_j}$ of the diagonal equations of order $ k,\;{b_1}p_1^k + \cdots + {b_s}p_s^k = m$. The bound obtained is $ {C^{{{(\log B)}^2}}} + C\vert m{\vert^{1/k}}$ where $ B = {\max _j}\{ e,\vert{b_j}\vert\} $ and $ C$ are positive constants depending at most on $ k$.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0854075-3
Keywords: Bounds for prime solutions, diagonal equations, trigonometric sums, Dirichlet's characters, the Hardy-Littlewood method
Article copyright: © Copyright 1986 American Mathematical Society