SMALL FRACTIONAL-PARTS OF ADDITIVE FORMS

被引：17

作者：

HARMAN, G

机构：

来源：

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 1993年 / 345卷 / 1676期

关键词：

D O I：

10.1098/rsta.1993.0132

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

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.

引用

页码：327 / 338

页数：12

共 19 条

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