The twisted fourth moment of the Riemann zeta function

DOI10.1515/CRELLE.2010.034zbMath1218.11076arXiv0709.2345MaRDI QIDQ3561029

C. P. Hughes, Matthew P. Young

Publication date: 17 May 2010

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/0709.2345

zbMATH Keywords

Riemann zeta-functionDirichlet polynomialstwisted fourth moment

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06)

Related Items (18)

On the zeros of Riemann's zeta-function on the critical line ⋮ Weighted value distributions of the Riemann zeta function on the critical line ⋮ Moments of the Hurwitz zeta function on the critical line ⋮ Shifted fourth moment of the Riemann zeta-function ⋮ The Mean Values of the Riemann Zeta-Function on the Critical Line ⋮ The mean square of the product of the Riemann zeta-function with Dirichlet polynomials ⋮ Upper bounds for fractional joint moments of the Riemann zeta function ⋮ On a Hybrid Fourth Moment Involving the Riemann Zeta-Function ⋮ The quantum unique ergodicity conjecture for thin sets ⋮ A WEIGHTED CENTRAL LIMIT THEOREM FOR log|ζ(1/2+it)| ⋮ The fourth moment of Dirichlet \(L\)-functions along the critical line ⋮ Moments and distribution of central \(L\)-values of quadratic twists of elliptic curves ⋮ Motohashi’s fourth moment identity for non-archimedean test functions and applications ⋮ On the splitting conjecture in the hybrid model for the Riemann zeta function ⋮ Fourth moment of the Riemann zeta-function with a shift along the real line ⋮ A quadratic divisor problem and moments of the Riemann zeta-function ⋮ Asymptotics for a class of arithmetic functions ⋮ Mean values of long Dirichlet polynomials with higher divisor coefficients

Cites Work

• A quadratic divisor problem
• More than one third of zeros of Riemann's zeta-function are on \(\sigma=1/2\)
• Kloosterman sums and a mean value for Dirichlet polynomials
• The Fourth Power Moment of the Riemann Zeta Function
• Power mean values of the Riemann zeta‐function
• Integral moments of L-functions
• Random matrix theory and \(\zeta(1/2+it)\).

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