Estimate for exponential sums and its applications

doi:10.1007/s11464-012-0222-5

Front Math Chin

2012, Vol. 7

Issue (4) : 765-783 https://doi.org/10.1007/s11464-012-0222-5

RESEARCH ARTICLE

Estimate for exponential sums and its applications

Weili YAO^1,2(

)

1. Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, China; 2. School of Mathematics, Shandong University, Jinan 250100, China

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Abstract

In this paper, we establish a new estimate on exponential sums by using the Bombieri-type theorem and the modified Huxley-Hooley contour. We also generalize the famous Goldbach-Vinogradov theorem, via different argument from that of Vinogradov. In particular, our major arcs are quite large and these enlarged major arcs are treated by the estimate we have established.

Keywords Exponential sum zero-density estimate circle method

Corresponding Author(s): YAO Weili,Email:yaoweili@shu.edu.cn

Issue Date: 01 August 2012

Cite this article:

Weili YAO. Estimate for exponential sums and its applications[J]. Front Math Chin, 2012, 7(4): 765-783.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-012-0222-5
https://academic.hep.com.cn/fmc/EN/Y2012/V7/I4/765

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