Related papers: Spectral determinants and quantum theta functions
We study theta functions of a Riemann surface of genus g from the view point of tau function of a hierarchy of soliton equations. We study two kinds of series expansions. One is the Taylor expansion at any point of the theta divisor. We…
We study relations between two fundamental constructions associated to vector bundles on a smooth complex projective curve: the theta function (a section of a line bundle on the moduli space of vector bundles) and the Szeg\"o kernel (a…
We first show that hypergeometric functions appear naturally as spectral functions when applying pseudo-differential calculus to decipher heat kernel asymptotic in the situation where the symbol algebra is noncommutative. Such observation…
In this paper presents the results obtained in the field of spectral theory operators of fractional differentiation. Proven a number of propositions which represents independent interest in the theory of fractional calculus. Introduced…
By the help of power series f we can naturally construct another power series that has as coefficients the absolute values of the coefficients of f. Utilising these functions we prove some inequalities for the spectral radius of the bounded…
In this paper, we study modular transformation properties of a certain class of functions with indefinite quadratic forms.
Spectral invariants are quantitative measurements in symplectic topology coming from Floer homology theory. We study their dependence on the choice of coefficients in the context of Hamiltonian Floer homology. We discover phenomena in this…
Let $\theta$ be an elementary theta function, such as the classical Jacobi theta function. We establish a spectral decomposition and surprisingly strong asymptotic formulas for $\langle |\theta|^2, \varphi \rangle$ as $\varphi$ traverses a…
Kernel matrices are of central importance to many applied fields. In this manuscript, we focus on spectral properties of kernel matrices in the so-called ``flat limit'', which occurs when points are close together relative to the scale of…
Continuing our study of spectral triples on quantum domains, we look at unbounded invariant and covariant derivations in the quantum annulus. In particular, we investigate whether such derivations can be implemented by operators with…
We study various properties of a nonperturbative partition function which can be associated to any spectral curve. When the spectral curve arises from a matrix model, this nonperturbative partition function is given by a sum of matrix…
Quantization and spectral properties of Toeplitz operators acting on spaces of pluriharmonic functions over bounded symmetric domains and $\mathbb C^n$ are discussed. Results are presented on the asymptotics \begin{align*} \|…
Spectral functions of symmetric matrices -- those depending on matrices only through their eigenvalues -- appear often in optimization. A cornerstone variational analytic tool for studying such functions is a formula relating their…
We study the moduli space of the spectral curves $y^2=W'(z)^2+f(z)$ which characterize the vacua of $\mathcal{N}=1$ U(n) supersymmetric gauge theories with an adjoint Higgs field and a polynomial tree level potential $W(z)$. It is shown…
We study the spectral functions, and in particular the zeta function, associated to a class of sequences of complex numbers, called of spectral type. We investigate the decomposability of the zeta function associated to a double sequence…
In 1994, Kac and Wakimoto found the denominator identity for classical affine Lie superalgebras, generalizing that for affine Lie algebras. As an application, they obtained power series identities for some powers of $\triangle(q)$, where…
The moment operators of a semispectral measure having the structure of the convolution of a positive measure and a semispectral measure are studied, with paying attention to the natural domains of these unbounded operators. The results are…
We study the spectral properties of curl, a linear differential operator of first order acting on differential forms of appropriate degree on an odd-dimensional closed oriented Riemannian manifold. In three dimensions its eigenvalues are…
In this paper we investigate the spectral and scattering theory for operators acting on topological crystals and on their perturbations. A special attention is paid to perturbations obtained by the addition of an infinite number of edges,…
The inclusion of the Gaussian-curvature term in the bulk of Polyakov-Kleinert string action renders new boundary terms and conditions by Gauss-Bonnet theorem. Within a leading approximation, the eigenmodes of smooth worldsheets and the…