On Character Sums and L-Series. II
On Character Sums and L-Series. II
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DOI：
10.1112/plms/s3-12.1.193
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发表时间：
1962
影响因子：
1.8
通讯作者：
D. A. Burgess
中科院分区：
文献类型：
--
作者：
D. A. Burgess
1.本文的主要结果是我在（1）中的特征和估计的进一步应用，即L-函数的一个估计。该估计的一个特定情况是，如果^是非主特征（mod&）并且Lx（s）是对应的X函数，则其中A<^ B是维诺格拉多夫的符号，表示|对于某个常数K，A\< KB，其中在这种情况下，K仅取决于t和e。以前给出的最精确的估计是H.达文波特（Davenport），1931年。本文的第一部分将致力于推广我的估计素模特征和复合模特征和。这种推广的主要困难是获得一个适当的估计，
1. THE principal result of this paper is a further application of my character sum estimate contained in (1), namely an estimate for L-functions. A particular case of this estimate is that if^ is a non-principal character (mod&) and Lx (s) is the corresponding X-function, then where A<^ B is Vinogradov's notation denoting| A\< KB for some constant K, and where in this case K depends only on t and e. Previously the sharpest estimate given wasThis was proved by H. Davenport (2) in 1931. The first part of the paper will be devoted to generalizing my estimates for prime modulus character sums to composite modulus character sums. The principal difficulty in this generalization is that of obtaining a suitable estimate for