Weighted fourth moments of Hecke zeta functions with groessencharacters

We use recently obtained bounds for sums of Kloosterman sums to bound the sum \(\sum_{-D\leq d\leq D} \int_{-D}^D |\zeta(1/2+it,\lambda^d)|^4| \sum_{01\), while the numbers \(D,M\in(0,\infty)\) and function \(A:{\Bbb Z}[i]-\{0\}\rightarrow{\Bbb C}\) are arbitrary (though it is only in respect of cas...

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Bibliographic Details
Published in:arXiv.org 2013-08
Main Author: Watt, Nigel
Format: Article
Language:English
Subjects:
Gaussian distribution
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Summary:We use recently obtained bounds for sums of Kloosterman sums to bound the sum \(\sum_{-D\leq d\leq D} \int_{-D}^D |\zeta(1/2+it,\lambda^d)|^4| \sum_{01\), while the numbers \(D,M\in(0,\infty)\) and function \(A:{\Bbb Z}[i]-\{0\}\rightarrow{\Bbb C}\) are arbitrary (though it is only in respect of cases in which \(M\) is relatively small, compared to \(D\), that our results are new and interesting). One of our new bounds may have an application in enabling a certain improvement of a result of P.A. Lewis on the distribution of Gaussian primes.
ISSN:2331-8422