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

2002/05/07 by Roelof W. Bruggeman, Bruggeman, Roelof W., Yoichi Motohashi +1 · 1 citation
Mathematics · #11F72 #11L05 #11M41 #22E30 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11F72 #msc:11L05 #msc:11M41 #msc:22E30

paper · pdf · doi:10.48550/arxiv.math/0205066

64 pages; Plain TeX

arxiv created 2002/05/07 · arxiv updated 2009/11/30

Abstract

We prove the Kloosterman-Spectral sum formula for PSL(2,Z[i])\PSL(2,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. This sum formula allows the extension of the spectral theory of Kloosterman sums to all algebraic number fields.

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