Related papers: Weyl's Law with Error Estimate

Let $Q (z)$ be a holomorphic Hecke cusp newform of square-free level and $u_j (z)$ traverse an orthonormal basis of Hecke--Maass cusp forms of full level. Let $1/4 + t_j^2$ be the Laplace eigenvalue $u_j (z)$. In this paper, we prove that…

We reconsider in some detail a construction allowing (Borel) convergence of an alternative perturbative expansion, for specific physical quantities of asymptotically free models. The usual perturbative expansions (with an explicit mass…

We calculate the conformal anomaly from 5d Weyl gravity (with broken conformal symmetry) which is conjectured to be supergravity dual to ${\cal N}=2$ superconformal field theory via AdS/CFT correspondence. Its comparison with ${\cal N}=2$…

We introduce a general algebraic decomposition of Riemann-like and Weyl-like tensors with respect to a non-null vector $u$. We derive Gauss, Codazzi and Ricci-type identities for the Weyl tensor, that allow to relate the components of the…

In this paper, we study the two-point Weyl Law for the Laplace-Beltrami operator on a smooth, compact Riemannian manifold $M$ with no conjugate points. That is, we find the asymptotic behavior of the Schwartz kernel, $E_\lambda(x,y)$, of…

By Weyl's asymptotic formula, for any potential $V$ whose negative part $V_-$ is an $L^{1+d/2}$-function, \begin{align*} \operatorname{Tr} [-h^2 \Delta + V]_- &= L_d^{\mathrm{cl}} h^{-d} \int \mathrm{d} x\,[V]_-^{1+\frac d 2} + \mathrm{o}…

We introduce a new family of operators in 4-dimensional pseudo-Riemannian manifolds with a non-vanishing Weyl scalar (non-degenerate spaces) that keep the conformal covariance of \emph{conformally covariant tensor concomitants}. A…

We prove that the condition \begin{equation} \sum_{n=1}^\infty\frac{1}{nw(n)}<\infty \end{equation} is necessary for an increasing sequence of numbers $w(n)$ to be an almost everywhere unconditional convergence Weyl multiplier for the…

We show that Weyl's law for the number and the Riesz means of negative eigenvalues of Schr\"odinger operators remains valid under minimal assumptions on the potential, the vector potential and the underlying domain.

Under a natural asumption on the drift, the law of the simple random walk on the multidimensional first quadrant conditioned to always stay in the first octant was obtained by O'Connell in [O]. It coincides with that of the image of the…

Let $A_f(1,n)$ be the normalized Fourier coefficients of a $GL(3)$ Maass cusp form $f$ and let $a_g(n)$ be the normalized Fourier coefficients of a $GL(2)$ cusp form $g$. Let $\lambda(n)$ be either $A_f(1,n)$ or the triple divisor function…

We show that the symmetry algebra of the $SL(2,R)_{k}/U(1)$ coset model is a non-linear deformation of $W_{\infty}$, characterized by $k$. This is a universal $W$-algebra which linearizes in the large $k$ limit and truncates to $W_{N}$ for…

We calculate the trace and axial anomalies of $\mathcal{N}=(2,2)$ superconformal theories with exactly marginal deformations, on a surface with boundary. Extending recent work by Gomis et al, we derive the boundary contribution that…

Let $(M,g)$ be a Zoll manifold, i.e., a smooth, compact, Riemannian manifold without boundary all of whose geodesics are closed with a minimal common period $T$. The positive definite Laplace-Beltrami operator has eigenvalues…

We prove the Weyl-von Neumann-Berg theorem for quaternionic right linear operators (not necessarily bounded) in a quaternionic Hilbert space: Let $N$ be a right linear normal (need not be bounded) operator in a quaternionic separable…

We establish the submaximal symmetry dimension for Riemannian and Lorentzian conformal structures. The proof is based on enumerating all subalgebras of orthogonal Lie algebras of sufficiently large dimension and verifying if they stabilize…

The vertex algebra W_{1+\infty,c} with central charge c may be defined as a module over the universal central extension of the Lie algebra of differential operators on the circle. For an integer n\geq 1, it was conjectured in the physics…

We introduce Weyl's scale invariance as an additional local symmetry in the standard model of electroweak interactions. An inevitable consequence is the introduction of general relativity coupled to scalar fields a la Dirac and an…

The main goal of our paper is to establish a connection between the Weyl modules of the current Lie superalgebras (twisted and untwisted) attached to $\mathfrak{osp}(1,2)$ and the nonsymmetric Macdonald polynomials of types $A_2^{(2)}$ and…

This thesis provides an explicit, general trace formula for the Hecke and Casimir eigenvalues of GL(2)-automorphic representations over a global field. In special cases, we obtain Selberg's original trace formula. Computations for the…