相关论文: ZEROS
Global mapping properties of the Riemann Zeta function are used to investigate its non trivial zeros.
The main purpose of this article is to get a handle on determining how far a non-rational singularity is from being rational, or in other words, introduce a measure of the failure of a singularity being rational.
Some hypotheses in modern theoretical physics that have not any experimental verification are listed. The goal of the paper is not to criticize or be lawyers any of these hypotheses. The purpose is focus physicists attention on that now…
This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…
The proof of the conjecture of the Birch and Swinnerton - Dyer is presented in the paper. The Riemann's hypothesis on the distribution of non-trivial zeroes of the zeta-function of Riemann, previously proven, is word to prove this…
The Riemann hypothesis, which states that the non-trivial zeros of the Riemann zeta function all lie on a certain line in the complex plane, is one of the most important unresolved problems in mathematics. Inspired by the P\'olya-Hilbert…
A recent result of Griffin, Ono, Rolen and Zagier on Jensen polynomials related with the Riemann zeta function is improved.
In this paper we provide a proof of the Riemann Hypothesis by relating the non-trivial zeros of the zeta function to a certain Sturm-Liouville eigenvalue problem on a finite interval.
The main aim of this paper is twofold. First we generalize, in a novel way, most of the known non-vanishing results for the derivatives of the Riemann zeta function by establishing the existence of an infinite sequence of regions in the…
The purpose of this article is to present closed forms for various types of infinite series involving Fibonacci (Lucas) numbers and the Riemann zeta function at integer arguments.
The goal of the paper is twofold: it aims to give an extensive set of tools and bibliography towards Nowicki's conjecture both in an associative setting; it establishes a new result about Nowicki's conjecture for the free metabelian Poisson…
The aim of this work is to improve some elementary results regarding both the Deuring-Phenomenon and the Heilbronn-Phenomenon. We will give better estimates regarding both the influence of zeros of the Riemann zeta function on the…
Some of my previous publications were incomplete in the sense that non trivial zeros belonging to a particular type of fundamental domain have been inadvertently ignored. Due to this fact, I was brought to believe that computations done by…
In these lectures we first review the important properties of the Riemann $\zeta$-function that are necessary to understand the nature and importance of the Riemann hypothesis (RH). In particular this first part describes the analytic…
These notes were written from a series of lectures given in March 2010 at the Universidad Complutense of Madrid and then in Barcelona for the centennial anniversary of the Spanish Mathematical Society (RSME). Our aim is to give an…
Hypothesis of Riemann is rejected by definition, because {\zeta}(s), where s zeros of {\zeta}(s)=0, is not be equal by definition to the particular sum, which it assumes to be equal. R(s) = 1/2 holds only for the zeros of {\zeta}(s) = 0 and…
This comment about the article "Hamiltonian for the Zeros of the Riemann Zeta Function", by C. M. Bender, D. C. Brody, and M. P. M\"uller, published recently in Phys. Rev. Lett. (Phys. Rev. Lett., 118, 130201, (2017)) gives arguments…
This is neither an elementary introduction to singularity theory nor a specialized treatise containing many new theorems. The purpose of this little book is to invite the reader on a mathematical promenade. We pay a visit to Hipparchus,…
This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also…
The zeros of classical Eisenstein series satisfy many intriguing properties. Work of F. Rankin and Swinnerton-Dyer pinpoints their location to a certain arc of the fundamental domain, and recent work by Nozaki explores their interlacing…