相关论文: ZEROS
A study of zero-dimensional theories, based on exact results, is presented. First, relying on a simple diagrammatic representation of the theory, equations involving the generating function of all connected Green's functions are…
This theorem is based on holomorphy of studied functions and the fact that near a singularity point the real part of some rational function can take an arbitrary preassigned value.
A formal theory of experimentation will be presented. Such a theory presents the necessary & sufficient conditions a world must satisfy in order to admit the use of the scientific method.
The Riemann Hypothesis is a conjecture made in 1859 by the great mathematician Riemann that all the complex zeros of the zeta function $\zeta(s)$ lie on the `critical line' ${Rl} s= 1/2$. Our analysis shows that the assumption of the truth…
The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings,…
A proof of the Riemann hypothesis using the reflection principle is presented.
The central idea of this article is to introduce and prove a special form of the zeta function as proof of Riemann's last theorem. The newly proposed zeta function contains two sub functions, namely $f_1(b,s)$ and $f_2(b,s)$. The unique…
This is a draft version of Part I of a three-part textbook on quantum field theory.
In this note, we derive and interpret hidden zeros of tree-level amplitudes of various theories, including Yang-Mills, non-linear sigma model, special Galileon, Dirac-Born-Infeld, and gravity, by utilizing universal expansions of tree-level…
We link together three themes which had remained separated so far: the Hilbert space properties of the Riemann zeros, the ``dual Poisson formula'' of Duffin-Weinberger (also named by us co-Poisson formula), and the ``Sonine spaces'' of…
This is the first of a series of papers that we intend to publish about the epistemology of fundamental physics in its current state. One of the main objectives of these papers is to improve our understanding of fundamental physics (and…
In this article, it is proved that the non-trivial zeros of the Riemann zeta function must lie on the critical line, known as the Riemann hypothesis.
We present a set of lectures on topics of advanced calculus in one real and complex variable with several new results and proofs on the subject, specially with detailed proof-always missing in the literature - of the Cissoti explicitly…
The goal of this work is to develop, in a systematic way and in a full natural generality, the foundations of a theory of functions of (free) noncommuting variables.
In this paper, we establish a simple criterion for two $L$-functions $L_1$ and $L_2$ satisfying a functional equation (and some natural assumptions) to have infinitely many distinct zeros. Some related questions have already been answered…
The purpose of the present paper is to reveal the relation between the behavior of the logarithm of the Riemann zeta-function $\log{\zeta(s)}$ and the distribution of zeros of the Riemann zeta-function. We already know some examples for the…
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
The paper gives an introduction to Steinberg groups for root graded Jordan pairs, a theory developed in the recent book "Steinberg groups for Jordan pairs" by Ottmar Loos and the author.
In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are…
This research paper presents the results of a study on the application of extended analytic continuation to locate the non-trivial zeros of the Riemann Hypothesis.