Mean values of the Riemann zeta-function and its derivatives
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Publication:788026
DOI10.1007/BF01403094zbMath0531.10040OpenAlexW2078065964MaRDI QIDQ788026
Publication date: 1984
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/143092
Related Items (60)
Sum of the Lerch Zeta-Function over Nontrivial Zeros of the Dirichlet $$\boldsymbol{L}$$ -Function ⋮ The behaviour of the Riemann zeta‐function on the critical line ⋮ Weighted value distributions of the Riemann zeta function on the critical line ⋮ Simple zeros of the zeta function of a quadratic number field. I ⋮ Mean values of derivatives of \(L\)-functions in function fields. I. ⋮ Applications of theL-functions ratios conjectures ⋮ Uniform distribution of the zeros of the Riemann zeta function and the mean value theorems of Dirichlet L-functions ⋮ On the error term \(\Delta_{(k,l)}(x)\) ⋮ On the vertical distribution of values of L-functions in the Selberg class ⋮ A discrete mean-value theorem for the higher derivatives of the Riemann zeta function ⋮ A hybrid Euler-Hadamard product for the Riemann zeta function ⋮ On the value distribution of two Dirichlet \(L\)-functions ⋮ NEGATIVE VALUES OF THE RIEMANN ZETA FUNCTION ON THE CRITICAL LINE ⋮ New results on the value distribution of the Riemann zeta-function on the critical line ⋮ Simple zeros of modular L -functions ⋮ Mean values of derivatives of \(L\)-functions in function fields. II. ⋮ Lower bounds of discrete moments of the derivatives of the Riemann zeta-function on the critical line ⋮ On some sums at thea-points of thek-th derivatives of the DirichletL-functions ⋮ Lower bounds for negative moments of ζ′(ρ)$\zeta ^{\prime }(\rho )$ ⋮ A WEIGHTED CENTRAL LIMIT THEOREM FOR log|ζ(1/2+it)| ⋮ Note on the mean values of derivatives of quadratic Dirichlet \(L\)-functions in function fields ⋮ Mean values of derivatives of L-functions in function fields: III ⋮ SUM OF VALUES OF THE IDEAL CLASS ZETA-FUNCTION OVER NONTRIVIAL ZEROS OF THE RIEMANN ZETA-FUNCTION ⋮ The generalized Riemann hypothesis from zeros of the zeta function ⋮ AN UPPER BOUND FOR DISCRETE MOMENTS OF THE DERIVATIVE OF THE RIEMANN ZETA‐FUNCTION ⋮ Upper bounds for discrete moments of the derivatives of the Riemann zeta-function on the critical line ⋮ A Discrete Mean Value of the Derivative of the Riemann Zeta Function ⋮ Mean values of derivatives of $L$-functions in function fields: IV ⋮ ON A NEW CIRCLE PROBLEM ⋮ Finite Euler products and the Riemann hypothesis ⋮ Large gaps between zeros of the zeta-function on the critical line and moment conjectures from random matrix theory ⋮ Value-distribution of the Riemann zeta-function along its Julia lines ⋮ Dirichlet series with periodic coefficients and their value-distribution near the critical line ⋮ On the zeros of the \(k\)-th derivative of the Riemann zeta function under the Riemann hypothesis ⋮ On Negative Moments of the Riemann Zeta‐Function ⋮ Some observations concerning the distribution of the zeros of the zeta functions. III ⋮ On the roots of the equation \(\zeta (s)=a\) ⋮ THE DISCRETE MEAN SQUARE OF THE DIRICHLET L-FUNCTION AT NONTRIVIAL ZEROS OF ANOTHER DIRICHLET L-FUNCTION ⋮ The fourth moment of \(\zeta'(\rho)\) ⋮ Unnamed Item ⋮ The sum involving derivative of \(\zeta(s)\) over simple zeros ⋮ On some averages at the zeros of the derivatives of the Riemann zeta-function ⋮ On the occurrence of the sine kernel in connection with the shifted moments of the Riemann zeta function ⋮ Discrete mean square of the Riemann zeta-function over imaginary parts of its zeros ⋮ On the value distribution of Hurwitz zeta-functions at the nontrivial zeros of the Riemann zeta-function ⋮ On the distribution of values of the derivative of the Riemann zeta function at its zeros. I ⋮ Mean square of the derivatives of Hardy's \(Z\)-function ⋮ Explicit formulae and discrepancy estimates for \(a\)-points of the Riemann zeta-function ⋮ Large gaps between zeros of the zeta‐function ⋮ Perturbation of scattering poles for hyperbolic surfaces and central values of \(L\)-series ⋮ An exact formula for a Lambert series associated to a cusp form and the Möbius function ⋮ Titchmarsh’s Method for the Approximate Functional Equations for , , and ⋮ On a certain sum of the derivative of Dirichlet \(L\)-functions ⋮ Lower bounds for discrete negative moments of the Riemann zeta function ⋮ On a sum involving the Möbius function ⋮ Simple zeros and discrete moments of the derivative of the Riemann zeta-function ⋮ On the distribution (mod 1) of the normalized zeros of the Riemann zeta-function ⋮ On the distribution of the \(a\)-points of a Selberg class \(L\)-function modulo one ⋮ Large values of Dirichlet L-functions at zeros of a class of L-functions ⋮ The average behaviour of the error term in a new kind of the divisor problem
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