A discrete mean value of the derivative of the Riemann zeta function’, preprint - Ng () Citation Context ...) = ∑ n≤N 0<γ≤T xn ns and Y (s) = ∑ are Dirichlet polynomials. For X(s) and Y (s) satisfying certain reasonable conditions, a general formula for S(X, Y ; T)...
For the Tornheim double zeta function T(s1,s2,s3) of complex variables,we obtain its functional equations,which are new.Using the calculus of r-th order derivative of zeta(s,alpha) as a function of alpha(developed in author[7])as the tool,we obtain with ease an expression for T(s,s...
摘要: Assuming the Riemann hypothesis we establish explicit bounds for the modulus of the log-derivative of Riemann's zeta-function in the critical strip.关键词: Zeta-function Riemann hypothesis Critical strip Beurling–Selberg extremal problem Bandlimited functions Exponential type DOI: 10.1007/s00209-...
For the Tornheim double zeta function T(s1,s2,s3) of complex variables,we obtain its functional equations,which are new.Using the calculus of r-th order derivative of zeta(s,alpha) as a function of alpha(developed in author[7])as the tool,we obtain with ease an expression for T(s,s...
Moments of the derivative of the riemann zeta-function and of characteristic polynomials - Conrey, Rubinstein, et al. - 2005 () Citation Context ...tter is known form our work [3] to be a special case of ˜ Ehard N (t; a, µ; ξ). The coefficients in the power series appear...
zeta function has many closely spaced zeros.This gives a condition on the zeros of the derivative of the zeta function which implies alower bound of the class numbers of imaginary quadratic f i elds.1. IntroductionThe spacing between zeros of the Riemann zeta-function and the location of ...
Taking further derivatives of eq. (7) then yields: ψ (n) (x) = d n+1 ln Γ(x) dx n+1 = (−1) n+1 n! ∞ k=0 1 (x +k) n+1 , n = 1, 2, 3, . . . If we set x = 1, then using the definition of the Riemann zeta function: ζ(n) = ∞ k=0 1 (k...
The Notes give a direct approach to the Selberg zeta-function for cofinite discrete subgroups of SL (2,#3) acting on the upper half-plane. The basic idea i... Jurgen Fischer - Springer-Verlag, 被引量: 101发表: 1987年 Factorization of the Heun's differential operator cases.3 Derivatives...
In this paper the fractional order derivative of a Dirichlet series, Hurwitz zeta function and Riemann zeta function is explicitly computed using the Caputo fractional derivative in the Ortigueira sense. It is observed that the obtained results are a natural generalization of the integer order derivat...
Berndt, Levinson, and Montgomery investigated the general case, meanwhile Akatsuka gave sharper estimates for the first derivative of the Riemann zeta function under the truth of the Riemann hypothesis. In this paper, we extend the results of Akatsuka to the second derivative of the Riemann zeta ...