Functiones et Approximatio Commentarii Mathematici

Sum formula for Kloosterman sums and fourth moment of the Dedekind zeta-function over the Gaussian number field

Roelof W. Bruggeman and Yoichi Motohashi

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Abstract

We prove the Kloosterman-Spectral sum formula for $\mathrm{PSL}_{2}(\mathbb{Z}[i])\backslash \mathrm{PSL}_{2}(\mathbb{C})$, and apply it to derive an explicit spectral expansion for the fourth power moment of the Dedekind zeta-function of the Gaussian number field.

Article information

Source
Funct. Approx. Comment. Math., Volume 31 (2003), 23-92.

Dates
First available in Project Euclid: 29 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.facm/1538186640

Digital Object Identifier
doi:10.7169/facm/1538186640

Mathematical Reviews number (MathSciNet)
MR2059538

Zentralblatt MATH identifier
1068.11057

Subjects
Primary: 11M41: Other Dirichlet series and zeta functions {For local and global ground fields, see 11R42, 11R52, 11S40, 11S45; for algebro-geometric methods, see 14G10; see also 11E45, 11F66, 11F70, 11F72} 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]
Secondary: 11F72: Spectral theory; Selberg trace formula 11L05: Gauss and Kloosterman sums; generalizations 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX]

Keywords
automorphic forms Dedekind zeta-function fourth moment Gaussian number field Kloosterman sums spectral theory sum formula

Citation

Bruggeman, Roelof W.; Motohashi, Yoichi. Sum formula for Kloosterman sums and fourth moment of the Dedekind zeta-function over the Gaussian number field. Funct. Approx. Comment. Math. 31 (2003), 23--92. doi:10.7169/facm/1538186640. https://projecteuclid.org/euclid.facm/1538186640


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