The Large Sieve Inequality for Algebraic Number Fields. II: Means of Moments of Hecke Zeta-Functions
The Large Sieve Inequality for Algebraic Number Fields. II: Means of Moments of Hecke Zeta-Functions
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DOI：
10.1112/plms/s3-21.1.108
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发表时间：
1970-07
影响因子：
1.8
通讯作者：
M. Huxley
中科院分区：
文献类型：
--
作者：
M. Huxley
S 2* IMH^ x)?< Q2 (\t\+ Wog*{Q (\t\+ 2)}(5) is implicit in his work. It will be noted that (4) is an improvement on (5) only if\t\< 4 Iog4 $. Paley and Linnik use elaborate analytical techniques to express L (s, x) as a short or a rapidly converging sum and use a crude argument in summing over characters, whilst Gallagher uses little analytic number theory other than the series definition of the.^-functions, but applies the large sieve to sums over the characters. HL Montgomery observed that the two methods could be combined, and in this paper we shall extend Montgomery's unpublished work to the zeta-functions of an algebraic number field K. For the rational field our result reduces to
