A New Application of the Hardy‐Littlewood‐Kloosterman Method
A New Application of the Hardy‐Littlewood‐Kloosterman Method
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DOI：
10.1112/plms/s3-12.1.425
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发表时间：
1962
影响因子：
1.8
通讯作者：
T. Estermann
中科院分区：
文献类型：
--
作者：
T. Estermann
KLOOSTERMAN(1)得到了方程ax2+ by2+ cz2+ dt2-n在整数x， y, z， t中的解个数渐近公式，其中a， b, c， d为正整数，n-»-ao。本文讨论了一个类似的问题。假设av a2 a3 a4和K为非零整数，并且前四个不全是正的也不全是负的。我将得到方程ax h^+ a2 h2 2+ a3 hz 2+ a4 h^= K（1.1）在正整数h1} hz， h3， h^中v (n)的解的渐近公式
KLOOSTERMAN (1) obtained an asymptotic formula for the number of solutions of the equation ax2+ by2+ cz2+ dt2—n in integers x, y, z, t, where a, b, c, d are given positive integers, and n-»-ao. This paper deals with a similar problem. It is assumed that av a2, a3, a4, and K are given non-zero integers, and that the first four are neither all positive nor all negative. I shall obtain an asymptotic formula for the number v (n) of solutions of the equation ax h^+ a2 h2 2+ a3 hz 2+ a4 h^= K(1.1) in positive integers h1} hz, h3, h^ for which