Results 141 to 150 of about 67,838 (152)

Zeros of the derivatives of the Riemann $ \xi$-function

Izvestiya: Mathematics, 2005
We show that the proportion of the zeros of the th derivative of the Riemann -function (where is an integer) that are on the critical line is greater than .
openaire   +1 more source

On simple zeros of derivatives of the Riemann $ \xi$-function

Izvestiya: Mathematics, 2006
We get a lower bound for the number of simple zeros of the function on the critical line, where .
openaire   +1 more source

The holomorphic flow of Riemann's function ξ(z)

Nonlinearity, 2005
Summary: The holomorphic flow \(\dot z=\xi(z)\) of Riemann's xi function is considered. Phase portraits are plotted and the following results, suggested by the portraits, proved: all separatrices tend to the positive and/or negative real axes. There are an infinite number of crossing separatrices.
openaire   +1 more source

A partial fraction expansion related to Riemann’s xi function

Boletín de la Sociedad Matemática Mexicana
Fil: Panzone, Pablo Andres. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática.
openaire   +2 more sources

On the zeros of the Riemann \(\xi\)-function

2003
In his paper [Pure Appl. Math. 6, No. 2, 6-12 (1990; Zbl 0862.11049)] \textit{P. C. Hu} showed that the Riemann hypothesis is equivalent to a certain sum over the zeros of the Riemann zeta function on the critical axis having a specific value; if the Riemann hypothesis were false then the value of the sum would be less than this value.
Csordas, George, Yang, Chung-Chun
openaire   +1 more source

On a Positivity Property of the Riemann ξ‐Function

Lithuanian Mathematical Journal, 2002
Let \(\xi(s)={1\over 2}s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s)\), and define \[ h(\sigma)=\inf\Biggl\{\Re\biggl({\xi'\over\xi}(\sigma+it)\bigg): -\inftya\); in particular, it holds for \(\sigma\geq 1\). Instead of appealing to the Riemann Hypothesis, the author uses the fact that the zeros are symmetrical with respect to the critical line.
openaire   +2 more sources

On the Asymptotic Behavior of the Riemann ξ-Function

American Journal of Mathematics, 1945
This asymptotic relation is a well-known result of Hadamard and is more than sufficient for his purpose in applying his theory of entire functions to the Riemann _-function.2 Actually, he defines M1(r) to be the maximum of f(s)I on the circle I= r, which does not affect the formula (1), but would affect the more delicate relations to be considered ...
openaire   +1 more source

The Riemann Xi Function

2017
openaire   +1 more source

A Note on the Riemann ξ-Function

Journal of the London Mathematical Society, 1935
openaire   +1 more source

On the Way to Riemann’s Entire Function $$\xi (s)$$

2021
openaire   +1 more source