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Small Gál sums and applications
Journal of the London Mathematical Society ( IF 1.0 ) Pub Date : 2020-09-07 , DOI: 10.1112/jlms.12378
Régis de la Bretèche 1 , Marc Munsch 2 , Gérald Tenenbaum 3
Affiliation  

In recent years, maximizing Gál sums regained interest due to a firm link with large values of L ‐functions. In the present paper, we initiate an investigation of small sums of Gál type, with respect to the L 1 ‐norm. We also consider the intertwined question of minimizing weighted versions of the usual multiplicative energy. We apply our estimates to: (i) a logarithmic refinement of Burgess' bound on character sums, improving previous results of Kerr, Shparlinski and Yau; (ii) an improvement on earlier lower bounds by Louboutin and the second author for the number of nonvanishing theta functions associated to Dirichlet characters; and (iii) new lower bounds for low moments of character sums.

中文翻译:

小盖尔总结和应用

近年来,最大化Gál的总金额重新获得了兴趣,这是由于与价格的较大价值建立了牢固的联系 大号 -职能。在本文中,我们将针对Gal类型的少量款项进行调查 大号 1个 -规范。我们还考虑了使最小乘积能量的加权形式最小化的问题。我们将估算结果应用于:(i)对Burgess的字符总和的对数改进,以改进Kerr,Shparlinski和Yau的先前结果;(ii)Louboutin和第二作者对与Dirichlet字符相关的不变的theta函数的数目的较早的下界进行了改进;(iii)在字符总和较低的时刻设置新的下限。
更新日期:2020-09-07
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