Related papers: Newforms and Spectral Multiplicities for $\Gamma_0…

We study the spectrum of the Laplace operator of a complete minimal properly immersed hypersurface $M$ in $\R^{n+1}$. (1) Under a volume growth condition on extrinsic balls and a condition on the unit normal at infinity, we prove that $M$…

In this paper, we prove a similar result to the fundamental theorem of regular surfaces in classical differential geometry, which extends the classical theorem to the entire class of singular surfaces in Euclidean 3-space known as frontals.…

Let G be a graph of given order and mu(G) be the largest eigenvalue of its adjacency matrix. We give conditions on mu(G) that imply Hamiltonicity of G and of its complement.

Dynamical degrees and spectra can serve to distinguish birational automorphism groups of varieties in quantitative, as opposed to only qualitative, ways. We introduce and discuss some properties of those degrees and the Cremona degrees,…

We compute spectra of symmetric random matrices defined on graphs exhibiting a modular structure. Modules are initially introduced as fully connected sub-units of a graph. By contrast, inter-module connectivity is taken to be incomplete.…

Symmetry invariants of a group specify the classes of quasiparticles, namely the classes of projective irreducible co-representations in systems having that symmetry. More symmetry invariants exist in discrete point groups than the full…

Let $f$ be a newform of weight $2$ on $\Gamma_0(N)$ with Fourier $q$-expansion $f(q)=q+\sum_{n\geq 2} a_n q^n$, where $\Gamma_0(N)$ denotes the group of invertible matrices with integer coefficients, upper triangular mod $N$. Let $p$ be a…

We investigate eigenvalues of the zero-divisor graph $\Gamma(R)$ of finite commutative rings $R$ and study the interplay between these eigenvalues, the ring-theoretic properties of $R$ and the graph-theoretic properties of $\Gamma(R)$. The…

Consider a fixed connected, finite graph $\Gamma$ and equip its vertices with weights $p_i$ which are non-negative integers. We show that there is a finite number of possibilities for the coefficients of the canonical cycle of a numerically…

We develop a new method for proving that a flow has the so-called strong convolution singularity property, i.e. the Gaussian system induced by its (reduced) maximal spectral type has simple spectrum. We use these methods to give examples of…

An approach, based on the Smith Normal Form, is introduced to study the spectra of symmetric matrices with a given graph. The approach serves well to explain how the path cover number (resp. diameter of a tree T) is related to the maximum…

Let $F \in S_{k_1}(\Gamma^{(2)}(N_1))$ and $G \in S_{k_2}(\Gamma^{(2)}(N_2))$ be two Siegel cusp forms over the congruence subgroups $\Gamma^{(2)}(N_1)$ and $\Gamma^{(2)}(N_2)$ respectively. Assume that they are Hecke eigenforms in…

Two dimensional conformal field theories with large central charge and a sparse low-lying spectrum are expected to admit a classical string holographic dual. We construct a large class of such theories employing permutation orbifold…

Firstly, we completely determine the self-similar Hausdorff spectrum of the group of $q$-adic automorphisms where $q$ is a prime power, answering a question of Grigorchuk. Indeed, we take a further step and completely determine its…

We study the spectral properties of certain non-self-adjoint matrices associated with large directed graphs. Asymptotically the eigenvalues converge to certain curves, apart from a finite number that have limits not on these curves.

Let $\pi$ be a cuspidal automorphic representation for GL(2)/$\mathbb{Q}$ that is self-dual. In this Note we show that there exists a positive upper Dirichlet density of primes at which the associated Hecke eigenvalues of $\pi$ are larger…

The paper gives a thorough introduction to spectra of digraphs via its Hermitian adjacency matrix. This matrix is indexed by the vertices of the digraph, and the entry corresponding to an arc from $x$ to $y$ is equal to the complex unity…

In the round 6-sphere, null-torsion holomorphic curves are fundamental examples of minimal surfaces. This class of minimal surfaces is quite rich: By a theorem of Bryant, extended by Rowland, every closed Riemann surface may be conformally…

Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which…

We establish the spectral gap property for dense subgroups of $SU(d)$ ($d\geq 2$), generated by finitely many elements with algebraic entries; this result was announced in [BG3]. The method of proof differs, in several crucial aspects, from…