Related papers: An adelic causality problem related to abelian L-f…
We prove polarity duality for covering problems in Hilbert geometry. Let $G$ and $K$ be convex bodies in $\mathbb{R}^d$ where $G \subset \operatorname{int}(K)$ and $\operatorname{int}(G)$ contains the origin. Let $N^H_K(G,\alpha)$ and…
We start from the pure Einstein-Hilbert action in Metric Affine Gravity, with the orthonormal metric. We get an effective Levi-Civita Dilaton gravity theory in which the Dilaton field is related to the scaling of the gravitational coupling.…
Through an equivalent condition on the Farey series set forth by Franel and Landau, we prove Riemann Hypothesis for the Riemann zeta-function and the Dirichlet L-function.
In this paper, we present some results for existence of global solutions and attractivity for mulidimensional fractional differential equations involving Riemann-Liouville derivative. First, by using a Bielecki type norm and Banach fixed…
Let K be an algebraic function field of characteristic 2 with constant field C_K. Let C be the algebraic closure of a finite field in K. Assume that C has an extension of degree 2. Assume that there are elements u,x of K with u…
Recently S. Patrikis, J.F. Voloch and Y. Zarhin have proven, assuming several well known conjectures, that the finite descent obstruction holds on the moduli space of principally polarised abelian varieties. We show an analogous result for…
We consider the Cauchy problem to the general defocusing and focusing $p\times q$ matrix nonlinear Schr\"{o}dinger (NLS) equations with initial data allowing arbitrary-order poles and spectral singularities. By establishing the…
We address the existence of global solutions to the initial value problem for the integrable nonlocal derivative nonlinear Schr\"{o}dinger equation in weighted Sobolev space $H^{2}(\mathbb{R})\cap H^{1,1}(\mathbb{R})$. The key to prove this…
Zurek's and Kibble's causal constraints for defect production at continuous transitions are encoded in the field equations that condensed matter systems and quantum fields satisfy. In this article we highlight some of the properties of the…
The expression of causality depends on an underlying choice of chronology. Since a chronology is provided by any Lorentzian metric in relativistic theories, there are as many expressions of causality as there are non-conformally related…
Let k be a field, and let {\pi}:\tilde{X} -> X be a proper birational morphism of irreducible k-varieties, where \tilde{X} is smooth and X has at worst quotient singularities. When the characteristic of k is zero, a theorem of Koll\'ar in…
We study the distribution of closed geodesics for the modular surface. We improve the error term in the prime geodesic theorem, and obtain results on prime geodesics in very short intervals conditionally on the generalized Riemann…
We construct an integrable physical model of a single particle scattering with impurities spread on a circle. The $S$-matrices of the scattering with the impurities are such that the quantized energies of this system, coming from the Bethe…
We find an infinite set of eigenfunctions for the Laplacian with respect to a flat metric with conical singularities and acting on degree zero bundles over special Riemann surfaces of genus greater than one. These special surfaces…
We give a complete solution to the Borel-Ritt problem in non-uniform spaces $\mathscr{A}^-_{(M)}(S)$ of ultraholomorphic functions of Beurling type, where $S$ is an unbounded sector of the Riemann surface of the logarithm and $M$ is a…
In this short note, we investigate the generalization of Lehmer's problem to finitely generated fields over $\mathbb{Q}$.
Universal extensions arise naturally in the Auslander bijections. For an abelian category having Auslander-Reiten duality, we exploit a bijection triangle, which involves the Auslander bijections, universal extensions and the…
Given a Hilbertian field $k$ and a finite set $\mathcal{S}$ of Krull valuations of $k$, we show that every finite split embedding problem $G \rightarrow {\rm{Gal}}(L/k)$ over $k$ with abelian kernel has a solu\-tion ${\rm{Gal}}(F/k)…
For a $\mathbb{R}^{k}-$action generated by vector fields $X_{1},...,X_{k}$ we define an operator $-(X_{1}^{2}+...+X_{k}^{2})$, the orbitwise laplacian. In this paper, we study and classify $\mathbb{R}^{k}-$actions whose orbitwise laplacian…
In this paper, we partially complete the local Rankin-Selberg theory of Asai $L$-functions and $\epsilon$-factors as introduced by Flicker and Kable. In particular, we establish the relevant local functional equation at Archimedean places…