A new approach to the spectral theory of the fourth moment of the Riemann zeta-function

DOI10.1515/crll.2005.2005.579.75zbMath1064.11059arXivmath/0310104OpenAlexW2138466450MaRDI QIDQ4654802

Yoichi Motohashi, Roelof Wichert Bruggeman

Publication date: 9 March 2005

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0310104

zbMATH Keywords

spectral theoryfourth momentRiemann's zeta-function

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items (15)

On Motohashi’s formula ⋮ The twelfth moment of central values of Hecke series ⋮ Fourier coefficients of Eisenstein series formed with modular symbols and their spectral decomposition ⋮ A note on the mean value of the zeta and \(L\)-functions. XIV ⋮ Non-split sums of coefficients of \(\mathrm{GL}(2)\)-automorphic forms ⋮ A duality relation for certain triple products of automorphic forms ⋮ The unipotent mixing conjecture ⋮ A note on the mean value of the zeta and \(L\)-functions. XV ⋮ The horocycle flow at prime times ⋮ The spectral decomposition of shifted convolution sums ⋮ The spectral decomposition of shifted convolution sums over number fields ⋮ Uniform bound for Hecke \(L\)-functions ⋮ Twisted \(L\)-functions over number fields and Hilbert's eleventh problem ⋮ Rankin-Selberg without unfolding and bounds for spherical Fourier coefficients of Maass forms ⋮ Motohashi’s formula for the fourth moment of individual DirichletL-functions and applications

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