Multiple Exponential Sums with Monomials and Their Applications in Number Theory
Multiple Exponential Sums with Monomials and Their Applications in Number Theory
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DOI：
10.1023/a:1006777803163
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发表时间：
2000-07
影响因子：
0.9
通讯作者：
P. Sargos;J. Wu
中科院分区：
文献类型：
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作者：
P. Sargos;J. Wu
对于单项式指数和，Fouvry和Iwaniec的方法（[6],[11]）关键地使用了一个间隔引理（m,q）：= (m+q)α - (m−q)α。通过引入一种接近曲线族的整数点的技术，我们改进了它们的结果，并处理了foru(m,n,q):=t(m,q)nβ的间距问题。最后，我们选择了四个经典的算术问题来说明我们的新结果。
Fouvry and Iwaniec's method ([6], [11]) for exponential sums with monomials uses, in a crucial way, a spacing lemma fort(m,q) := (m+q)α− (m−q)α. By introducing a technique on integer points close to a family of curves, we are able to improve their result and to treat the spacing problem foru(m,n,q) :=t(m,q)nβ. Finally we choose four classic arithmetic problems to illustrate our new results.