A note on exponential sums over subgroups of and their applications

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• 作者：Binbin Zhou
• 关键词：Exponential sums ; Erdö ; s– ; Szemeré ; di Conjecture ; Subgroup
• 刊名：Journal of Number Theory
• 出版年：2010
• 出版时间：November 2010
• 年：2010
• 卷：130
• 期：11
• 页码：2467-2479
• 全文大小：198 K

文摘

Let G be a subgroup of , and #G=t, set , and . As q=p², we obtain the general cases of T_k(G), then one can easily obtain the nontrivial bound of S(G) as p^2/3+<tp, which improves t>p^7/10 from Malykhin (2005) [12]. On the other hand, it is known J. Bourgain obtain the nontrivial bound for t>p with arbitrary >0 by the sum-product method, however his bounds not be explicit. We also give some connections between T_k(G) and Erdös–Szemerédi Conjecture.