Related papers: The Spectrum of $\mathbb{Q}$-Isotropic Binary Quad…

Let $Q(x,y)$ be a quadratic form with discriminant $D\neq 0$. We obtain non trivial upper bound estimates for the number of solutions of the congruence $Q(x,y)\equiv\lambda \pmod{p}$, where $p$ is a prime and $x,y$ lie in certain intervals…

Lattice calculations allow us to probe the low-lying, non-perturbative spectrum of QCD using first principles numerical methods. Here we present the low-lying spectrum in the scalar sector with vacuum quantum numbers including, in fully…

We prove that the representations numbers of a ternary definite integral quadratic form defined over F_q[t], where F_q is a finite field of odd characteristic, determine its integral equivalence class when q is large enough with respect to…

The spectral problem for the q-Knizhnik-Zamolodchikov equations for $U_{q}(\widehat{sl_2}) (0<q<1)$ at arbitrary level $k$ is considered. The case of two-point functions in the fundamental representation is studied in detail.The scattering…

We are concerned with the acoustic scattering problem, at a frequency $\kappa$, by many small obstacles of arbitrary shapes with impedance boundary condition. These scatterers are assumed to be included in a bounded domain $\Omega$ in…

We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…

A simple formulation of an exactly integrable $q$-oscillator model on two dimensional lattice (in 2+1 dimensional space-time) is given. Its interpretation in the terms of 2d quantum inverse scattering method and nested Bethe Ansatz…

We extract an exact formula relating the number of lattice points in an expanding region of a complex semi-simple symmetric space and the automorphic spectrum from a spectral identity, which is obtained by producing two expressions for the…

This paper means to correct an error by the authors for the composite $q$ case in the paper "Lens Spaces, Isospectral on Forms but not on Functions", published in LMS J. Comput. Math.} 9 (2006), 270-286. All calculations and examples…

The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter $\Lambda$…

We study scalar conformal field theories whose large $N$ spectrum is fixed by the operator dimensions of either Ising model or Lee-Yang edge singularity. Using numerical bootstrap to study CFTs with $S_N\otimes Z_2$ symmetry, we find a…

We construct infinitely many examples of pairs of isospectral but non-isometric $1$-cusped hyperbolic $3$-manifolds. These examples have infinite discrete spectrum and the same Eisenstein series. Our constructions are based on an…

Using lattice homology, we give an explicit combinatorial description of the Seiberg-Witten-Floer spectrum $\mathit{SWF}(Y)$ for $Y$ an almost-rational plumbed homology sphere. This class of manifolds includes all Seifert fibered rational…

Let Q(u,v) be a positive definite binary quadratic form with arbitrary real coefficients. For large real x, one may ask for the number B(x) of primitive lattice points (integer points (m,n) with gcd(m,n) = 1) in the ellipse disc Q(u,v) < x,…

We study an intrinsic Lagrange spectrum of the unit circle $|z|=1$ in the complex plane with respect to the Eisensteinian field $\mathbb{Q}(\sqrt{-3})$. We prove that the minimum of the Lagrange spectrum is $2$ and that its smallest…

We derive the spectrum in the broken phase of a $\lambda\phi^4$ theory, in the limit $\lambda\to\infty$, showing that this goes as even integers of a renormalized mass in agreement with recent lattice computations.

We compute the asymptotics of the number of integral quadratic forms with prescribed orthogonal decompositions and, more generally, the asymptotics of the number of lattice points lying in sectors of affine symmetric spaces. A new key…

We show that the isotropic lines in the lattice Z_{d}^{2} are the Lagrangian submodules of that lattice and we give their number together with the number of them through a given point of the lattice. The set of isotropic lines decompose…

We construct a version of rational Symplectic Field Theory for pairs $(X,L)$, where $X$ is an exact symplectic manifold, where $L\subset X$ is an exact Lagrangian submanifold with components subdivided into $k$ subsets, and where both $X$…

An extended two-hadron operator is developed to extract the spectra of irreducible representations (irreps) in the finite volume. The irreps of the group for the finite volume system are projected using a coordinate-space operator. The…