Small fractional parts of additive forms
Small fractional parts of additive forms
复制标题
加法形式的小分数部分
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
G. Harman
中科院分区：
文献类型：
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作者：
G. Harman
我们展示了如何沃恩和伍利，这已被证明是富有成效的处理华林的问题，也可以用来调查分数部分的添加剂形式的方法。得到的结果是接近最好的可能的形式与代数系数。在一般情况下也得到了新的结果。扩展给出了几个加法形式同时小。在这项工作的关键成分是：平均值定理的指数和，使用一个小的共同因素的整数变量，和大筛不等式。
We show how the methods of Vaughan & Wooley, which have proved fruitful in dealing with Waring’s problem, may also be used to investigate the fractional parts of an additive form. Results are obtained which are near to best possible for forms with algebraic coefficients. New results are also obtained in the general case. Extensions are given to make several additive forms simultaneously small. The key ingredients in this work are: mean value theorems for exponential sums, the use of a small common factor for the integer variables, and the large sieve inequality.