设 p 是一个奇素数.对任意满足1≤a≤p-1的整数 a, 存在唯一的整数1≤a≤p-1, 使得 a ·a≡1mod p成立.设 N(p)表示区间 1≤a≤p-1中所有满足条件a与a具有相反奇偶性的a的集合.本文利用解析方法以及广义 Kloosterman和∑的性质研究一类特殊的Gauss和∑a∈N(p) χ(a)e((ma)/p)的估计问题, 给出一个较强的上界估计,其中e(x)=e2π#/emem#x,(m,p)=1, 且 χ是模p的任意特征.
Abstract
Let p be an odd prime.For each integer a with 1≤a≤p-1, we know that there exists one and only one a with 1≤a≤p-1 such that a ·a ≡1 mod p.Let N(p) denote the set of all integers 1 ≤ a ≤ p -1 in which a and a are of opposite parity.The main purpose of this paper is using the analytic method and the properties of general Kloosterman sums to study the estimate problem of the Gauss sums ∑a∈N(p) χ(a)e((ma)/p), and give a sharp upper bound estimate for it, where e(x)=e2π#/emem#x,(m,p)=1, and χ denotes any character mod p.
关键词
Lehmer数 /
Gauss和 /
广义Kloosterman和 /
上界估计
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Key words
Lehmer numbers /
Gauss sums /
general Kloosterman sums /
upper bound estimate
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参考文献
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脚注
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基金
国家自然科学基金项目(11226038, 11371012);陕西省教育厅专项基金(11Jk0472,11Jk0474);西安工程大学博士科研基金(BS1016)
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