Results 41 to 50 of about 5,228,205 (65)

Vanishing of the integral of the Hurwitz zeta function [PDF]

, 2002
A proof is given that the improper Riemann integral of δ(s, a) with respect to the real parameter a, taken over the interval (0, 1], vanishes for all complex s with R(s) < 1.
Kevin A. Broughan, Broughan, Kevin A.
core   +1 more source

The Carlson‐type zero‐density theorem for the Beurling ζ function

Journal of the London Mathematical Society
Abstract In a previous paper, we proved a Carlson‐type density theorem for zeroes in the critical strip for the Beurling zeta functions satisfying Axiom A of Knopfmacher. There we needed to invoke two additional conditions: the integrality of the norm (Condition B) and an “average Ramanujan condition” for the arithmetical function ...
openaire   +2 more sources

The Denseness of the Closure of Some Nyman–Beurling Linear Manifolds Implies the Absence of Zeroes of Certain Combinations of Riemann Zeta-Functions in the Critical Strip

Symmetry
The famous Nyman–Beurling theorem states that the absence of zeroes in the Riemann zeta-function in the half-plane Res > 1/p, p > 1, is equivalent to the circumstance in which the closure of the linear manifold of the functions f(x)=∑k=1nαkϑkx, where 0<ϑk≤1, with the condition ∑k=1nakϑk=0, is dense in Lp(0,1). Here, we show that if the closure
openaire   +2 more sources

A foundation monograph of Ipomoea (Convolvulaceae) in the New World. [PDF]

PhytoKeys, 2020
Wood JRI, Muñoz-Rodríguez P, Williams BRM, Scotland RW.   +3 more
europepmc   +1 more source

AN EXPOSITION OF THE RIEMANN ZETA FUNCTION

, 2023
This thesis is an exposition of the Riemann zeta function. Included are techniques of analytic continuation and relationships to special functions.
Molokach, John, NC DOCKS at East Carolina University   +1 more
core  

Some Convexity Properties of Dirichlet Series with Positive Terms [PDF]

, 2005
Some basic results for Dirichlet series ψ with positive terms via log-convexity properties are pointed out. Applications for Zeta, Lambda and Eta functions are considered.
Cerone, Pietro, Dragomir, Sever S
core   +2 more sources

Oscillation of the remainder term in the prime number theorem of Beurling, "caused by a given zeta-zero"

, 2022
Continuing previous study of the Beurling zeta function, here we prove two results, generalizing long existing knowledge regarding the classical case of the Riemann zeta function and some of its generalizations.
Révész, Szilárd Gy.
core  

Gram lines and the average of the real part of the Riemann zeta function [PDF]

, 2011
The contours ξ Λ(s) = 0 of the function which satisfies ζ(1-s) = Λ(s)ζ(s) cross the critical strip on lines which are almost horizontal and straight, and which cut the critical line alternately at Gram points and points where ζ(s) is imaginary.
Barnett, A. Ross, Broughan, Kevin A.
core  

New zero-density estimates for the Beurling $ζ$ function [PDF]

In two previous papers the second author proved some Carlson type density theorems for zeroes in the critical strip for Beurling zeta functions satisfying Axiom A of Knopfmacher.
Pintz, János, Révész, Szilárd Gy.
core   +1 more source

Approximation by Beurling zeta-functions

openaire   +1 more source