Related papers: On the generalized Riemann hypothesis II
A correction is brought to the opinion expressed in a previous note published in this journal that the off critical line points indicated by some authors as being non trivial zeros of the Davenport and Heilbronn function are affected of…
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.
This short note presents a peculiar generalization of the Riemann hypothesis, as the action of the permutation group on the elements of continued fractions. The problem is difficult to attack through traditional analytic techniques, and…
We correct a small gap found in the authors' paper 'On bounds for the effective differential Nullstellensatz' (J Algebra 449:1-21, 2016). This gap is due to an inequality that does not generally hold. However, under one additional…
In preparing the paper "Some extensions of Hilbert-Kunz multiplicity", we had occasion to perform an intricate set of computations pertaining to a single illustrative example. In the end, we have decided not to include the computations in…
Riemann conjectured that all the zeros of the Riemann $\Xi$-function are real, which is now known as the Riemann Hypothesis (RH). In this article we introduce the study of the zeros of the truncated sums $\Xi_N(z)$ in Riemann's uniformly…
A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…
The present preprint completes the arXiv preprint #2202.11652, entitled "Pseudodifferential arithmetic and the Riemann hypothesis", devoted to a proof of the conjecture. The first 4 pages of that preprint were devoted to a set of necessary…
Numerical study of the distribution of the Riemann zeros differences following the work [1] shows the significance of the function for which the prime sum expression is proposed. Computational results related to this definition explored…
This paper is a summary of the general approach outlined in my previous papers toward proving the riemann hypothesis. Numerical and graphical proof of the Riemann Hypothesis is presented with analytical arguments although more work needs…
Fundamental domains are found for functions defined by general Dirichlet series and using basic properties of conformal mappings the Great Riemann Hypothesis is studied.
In this article we obtain large deviation estimates for zeros of random holomorphic sections on punctured Riemann surfaces. These estimates are then employed to yield estimates for the respective hole probabilities. A particular case of…
We comment on some apparently weak points in the novel strategies recently developed by various authors aiming at a proof of the Riemann hypothesis. After noting the existence of relevant previous papers where similar tools have been used,…
S.E. Hans paper, Remarks on Pseudocovering Spaces in a Digital Topological Setting: A Corrigendum, is meant to address errors in previous papers. However, this paper is also marked by errors in its mathematics, as well as improprieties in…
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…
This paper is divided into two independent parts. The first part presents new integral and series representations of the Riemaan zeta function. An equivalent formulation of the Riemann hypothesis is given and few results on this formulation…
The paper is devoted to counterexamples involving the triviality of domains of products and/or adjoints of densely defined operators.
[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignant weight functions. These inequalities prolongate classical…
This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at…
Expected duality and approximation properties are shown to fail on Bergman spaces of domains in $\mathbb{C}^n$, via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation…