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

R.W. Bruggeman; Y. Motohashi

doi:10.7169/facm/1538186640

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

R.W. Bruggeman
, Y. Motohashi

Nihon University

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We prove the Kloosterman-Spectral sum formula for PSL2(Z[i])∖PSL2(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.

Original language	English
Pages (from-to)	23-92
Number of pages	70
Journal	Functiones et Approximatio
Volume	31
DOIs	https://doi.org/10.7169/facm/1538186640
Publication status	Published - 2003

Keywords

Mathematics
Wiskunde en computerwetenschappen
Landbouwwetenschappen
Wiskunde: algemeen

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03BrMo_sfGnfFinal published version, 1.66 MB

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

abstract = "We prove the Kloosterman-Spectral sum formula for PSL2(Z[i])∖PSL2(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.",

keywords = "Mathematics, Wiskunde en computerwetenschappen, Landbouwwetenschappen, Wiskunde: algemeen",

author = "R.W. Bruggeman and Y. Motohashi",

year = "2003",

doi = "10.7169/facm/1538186640",

language = "English",

volume = "31",

pages = "23--92",

journal = "Functiones et Approximatio",

issn = "0208-6573",

publisher = "Adam Mickiewicz University",

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T1 - Sum formula for Kloosterman sums and the fourth moment of the Dedekind zeta-function over the Gaussian number field

AU - Bruggeman, R.W.

AU - Motohashi, Y.

PY - 2003

Y1 - 2003

N2 - We prove the Kloosterman-Spectral sum formula for PSL2(Z[i])∖PSL2(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.

AB - We prove the Kloosterman-Spectral sum formula for PSL2(Z[i])∖PSL2(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.

KW - Mathematics

KW - Wiskunde en computerwetenschappen

KW - Landbouwwetenschappen

KW - Wiskunde: algemeen

U2 - 10.7169/facm/1538186640

DO - 10.7169/facm/1538186640

M3 - Article

SN - 0208-6573

VL - 31

SP - 23

EP - 92

JO - Functiones et Approximatio

JF - Functiones et Approximatio

ER -

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

Abstract

Keywords

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