Results 141 to 150 of about 66,497 (169)
On the distribution of zero points of a function which is related to Riemann's \(\xi\)-function
, 1951 openaire +2 more sources
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 .
Irina Sergeevna Rezvyakova
openalex +3 more sources
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 .
Irina Sergeevna Rezvyakova
openalex +3 more sources
Some of the next articles are maybe not open access.
Related searches:
Related searches:
On a positivity property of the Riemann \(\xi\)-function
Lithuanian Mathematical Journal, 2002Let \(\xi(s)={1\over 2}s(s-1)\pi^{-s/2}\Gamma(s/2)\zeta(s)\), 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 +3 more sources
On the zeros of the Riemann \(\xi\)-function
2003In 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 the Asymptotic Behavior of the Riemann ξ-Function
American Journal of Mathematics, 1945This 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 +2 more sources
A Note on the Riemann ξ-Function [PDF]
Journal of the London Mathematical Society, 1935 openaire +1 more source
Local Symmetry Defects in the Logarithmic Derivative of the Riemann Xi Function
We investigate a localized symmetry defect in the real part of the logarithmic deriva-tive of the Riemann xi function ξ(s). The identity ℜ (ξ′/ξ(s)) + ℜ (ξ′/ξ(1 − s)) = 0follows from the functional equation of ξ(s) and holds pointwise outside the zero set.We define this identity in the sense of tempered distributions on R by fixing ℜ(s) = σand ...openaire +1 more source