Related papers: Criteria equivalent to the Riemann Hypothesis
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 Appendix of the article arXiv:1212.5056 [math.CO] "On growth in an abstract plane" by Nick Gill, H. A. Helfgott, Misha Rudnev, contains a general "geometric Ruzsa triangle inequality" in a Desarguesian projective plane. The purpose of…
We consider the Riesz and Hardy-Littlewood wave i.e. a ``critical function'' whose behaviour is concerned with the possible truth of the Riemann Hypothesis (RH). The function is studied numerically for the case alpha = 15/2 and beta = 4 in…
This paper is a companion paper to [Lipman and Daubechies 2011]. We provide numerical procedures and algorithms for computing the alignment of and distance between two disk type surfaces. We provide a convergence analysis of the discrete…
We show the equivalence of admissibility conditions proposed by Wilcox and Yu and by Rui and Xu for the parameters of cyclotomic BMW algebras.
This is the text of my talk at CMU on Feb. 4, 2010 were I gave the second public presentation of the Univalence Axiom (called "equivalence axiom" in the text). The first presentation of the axiom was in a lecture at LMU Munich in November…
We develop a theoretical framework that allows us to compare electromagnetism and gravitation in a fully covariant way. This new scenario does not rely on any kind of approximation nor associate objects with different operational meaning as…
We establish sharp pointwise inequalities for the Riesz potential and its gradient in $\mathbb{R}^{n}$ and indicate their usefulness for potential analysis, moment theory and other applications.
In his comment, Riemann defends the conventional kinetic Bohm criterion on the basis that the underlying approximations become rigorous in the limit \lambda_D/l \rightarrow 0, where \lambda_D is the Deybe length and l is a collision length…
The semi-group of weighted composition operators $(W_n)_{n\geq 1}$ where \[ W_nf(z)=(1+z+\ldots+z^{n-1})f(z^n) \] on the classical Hardy-Hilbert space $H^2$ of the open unit disk is related to the Riemann Hypothesis (RH) (see…
This is the author's Ph.D. thesis, submitted to the University of Leipzig. It deals with the $L^2$ Riemannian metric on the manifold of all smooth Riemannian metrics on a fixed closed, finite-dimensional manifold. The main body of the…
We prove sectional and Ricci-type comparison theorems for the existence of conjugate points along sub-Riemannian geodesics. In order to do that, we regard sub-Riemannian structures as a special kind of variational problems. In this setting,…
We show that in the analytic category, given a Riemannian metric $g$ on a hypersurface $M\subset \Z$ and a symmetric tensor $W$ on $M$, the metric $g$ can be locally extended to a Riemannian Einstein metric on $Z$ with second fundamental…
A strategy for proving Riemann hypothesis is suggested. The vanishing of the Rieman Zeta reduces to an orthogonality condition for the eigenfunctions of a non-Hermitian operator $D^+$ having the zeros of Riemann Zeta as its eigenvalues. The…
In this paper we give a criterion that characterizes equivalent weak crossed products. By duality, we obtain a similar result for weak crossed coproducts and, as a consequence, we find the conditions that assures the equivalence between two…
Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We consider the…
We initiate a deep study of {\em Riesz MV-algebras} which are MV-algebras endowed with a scalar multiplication with scalars from $[0,1]$. Extending Mundici's equivalence between MV-algebras and $\ell$-groups, we prove that Riesz MV-algebras…
In their 1991 and 1993 foundational monographs, David and Semmes characterized uniform rectifiability for subsets of Euclidean space in a multitude of geometric and analytic ways. The fundamental geometric conditions can be naturally stated…
We give sufficient conditions for the exponential system to be a Riesz basis in $L^2(E)$, where $E$ is a union of two intervals. We show that these conditions are close to be necessary. In addition, we demonstrate ``extra point effect'' for…
Exact and asymptotic formulae are displayed for the coefficients $\lambda_n$ used in Li's criterion for the Riemann Hypothesis. For $n \to \infty$ we obtain that if (and only if) the Hypothesis is true, $\lambda_n \sim n(A \log n +B)$ (with…