The behaviour of the Riemann zeta‐function on the critical line

DOI10.1112/S0025579300007762zbMath1134.11337MaRDI QIDQ4786369

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Publication date: 15 December 2002

Published in: Mathematika (Search for Journal in Brave)

zbMATH Keywords

critical linezeros of the Riemann zeta-functionmaxima between successive zeros

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26)

Related Items (20)

Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function ⋮ Some four dimensional definite integrals arising from zeta-function theory ⋮ A note on the zeros of the derivatives of Hardy's function Z(t)$Z(t)$ ⋮ On the derivatives of Hardy's function Z(t) ⋮ Applications of Wirtinger inequalities on the distribution of zeros of the Riemann zeta-function ⋮ Mean of the product of derivatives of Hardy's \(Z\)-function with Dirichlet polynomial ⋮ The Second Moment of the First Derivative of Hardy’s Z-Function ⋮ Unnamed Item ⋮ Gaps between zeros of Dedekind zeta-functions of quadratic number fields ⋮ Large spaces between the zeros of the Riemann zeta-function and random matrix theory ⋮ The fourth moment of \(\zeta'(\rho)\) ⋮ Some mean value results related to Hardy's function ⋮ Mean square of the derivatives of Hardy's \(Z\)-function ⋮ Titchmarsh’s Method for the Approximate Functional Equations for , , and ⋮ Unnamed Item ⋮ Simple zeros and discrete moments of the derivative of the Riemann zeta-function ⋮ Gaps between zeros of \(\mathrm{GL}(2)\) \(L\)-functions ⋮ A Wirtinger type inequality and the spacing of the zeros of the Riemann zeta-function ⋮ The average behaviour of the error term in a new kind of the divisor problem ⋮ Generalized Wirtinger inequalities, random matrix theory, and the zeros of the Riemann zeta-function.

Cites Work

• Unnamed Item
• Hardy's inequality and its extensions
• Mean values of the Riemann zeta-function and its derivatives
• ON THE DISTRIBUTION OF GAPS BETWEEN ZEROS OF THE ZETA-FUNCTION
• A Note on Gaps between Zeros of the Zeta Function
• A Mean Value Theorem for the Riemann Zeta-Function at its Relative Extrema on the Critical Line
• THE FOURTH MOMENT OF DERIVATIVES OF THE RIEMANN ZETA-FUNCTION
• The Fourth Power Moment of the Riemann Zeta Function
• THE APPROXIMATE FUNCTIONAL EQUATION FOR ζ²(s)

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