Riemann zeta functionDirichlet L-functionthe pair correlationzeros11M26The aim of the present essay is to investigate whether it is possible to approach the age-old problem of the Hypothesis by elementary algebraic means. However, the results about the properties of the Zeta Function acquired by ...
J. Guillera, Some sums over the non-trivial zeros of the Riemann zeta function, Unpublished paper available at arXiv:1307.5723, (2013-2014).J. Guillera. Some sums over the non-trivial zeros of the Riemann zeta function. http://arxiv.org/abs/1307.5723v7, July 2013....
On the zeros of Riemann's zeta-function on the critical line We combine the mollifier method with a zero detection method of Atkinson to prove in a new way that a positive proportion of the nontrivial zeros of the Ri... Baluyot,AC Siegfred - 《Journal of Number Theory》 被引量: 24发...
For 0< α≤1 and 0< λ≤1, λ rational, we consider the sum of values of the Lerch zeta-function L ( λ , α , s ) taken at the nontrivial zeros of the Dirichlet L -function L ( s , χ ), where \\(\\chi \\bmod Q\\) , Q ≥1, is a primitive Dirichlet character....
The Riemann Hypothesis: A Qualitative Characterization of the Nontrivial Zeros of the Riemann Zeta Function Using Polylogarithms 来自 arXiv.org 喜欢 0 阅读量: 48 作者: L Fekih-Ahmed 摘要: We formulate a parametrized uniformly absolutely globally convergent series of ζ(s) denoted by Z(s, x...
On estimation of the difference $|Li(x)-\\pi(x)|$, on primes in short intervals, and distribution of nontrivial zeros of the Riemann zeta function... S Tan - 《Arxiv General Mathematics》 被引量: 0发表: 2020年 A note on Fourier coefficients of Hecke eigenforms in short intervals In...
The spacing intervals of adjacent Riemann zeta zeros (non-trivial) exhibit fractal (irregular) fluctuations generic to dynamical systems in nature such as fluid flows, heart beat patterns, stock market price index, etc., and are associated with unpredictability or chaos. The power spectra of such...
T. Nakamura and Lukasz Pan´kowski, On complex zeros off the critical line for non-monomial polynomial of zeta-functions, submitted, (2012), arXiv:1212.5890.T. Nakamura and L. Pankowski, On complex zeros off the critical line for non-monomial polynomial of zeta-functions, preprint....
On the Riemann zeta-function and analytic characteristic functions r(s) extends to an entire function in s on C. Define q(s) := (2π)−sΓ(s)r(s). The functional equation is q(12 − s) = q(s). Ramanujan Conjecture. (RC) The non-trivial zeros z of the Ramanujan function,...
(12) from Proposition 7, we know that →∑n=1-1/21n2=-π23→∑n=1-1/21=-12→∑n=1-1/2n2k=0,so all the fractional sums →∑n=1-1/2n2k disappear for positive integers k (because of the trivial zeroes of the Riemann Zeta function), and only finitely many terms survive: S(...