Estimate for exponential sums and its applications |
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Authors: | Weili Yao |
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Affiliation: | 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. |
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Keywords: | Exponential sum zero-density estimate circle method |
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