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Minima of Positive Definite Quadratic Forms
In Chapter 2 we defined Hermite’s constant \(\gamma _n\) ,...
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Positive Semi-Definite Matrices
The present chapter deals essentially with positive semi-definite matrices. It is the longest chapter of the book, but the reader should be aware...
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Theta functions of nineteen non-diagonal positive-definite quaternary quadratic forms of discriminant 784 with levels 28 or 56
We explore the theta functions of nineteen positive-definite integral non-diagonal quaternary quadratic forms of discriminant 784 with levels 28 or...
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Infinite-dimensional distances and divergences between positive definite operators, Gaussian measures, and Gaussian processes
This paper presents a survey of recent results on the generalization of distances and divergences on the set of symmetric, positive definite (SPD)...
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Definite orthogonal modular forms: computations, excursions, and discoveries
We consider spaces of modular forms attached to definite orthogonal groups of low even rank and nontrivial level, equipped with Hecke operators...
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A modified improved alternating positive semi-definite splitting preconditioner for double saddle point problems
In this paper, to further enhance the efficiency of the improved alternating positive semi-definite splitting (IAPSS) preconditioner proposed by Ren...
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Positive definiteness of real quadratic forms resulting from the variable-step L1-type approximations of convolution operators
The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-step** schemes...
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Two-Variable Wasserstein Means of Positive Definite Operators
We investigate the two-variable Wasserstein mean of positive definite operators, as a unique positive solution of the nonlinear equation obtained...
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Entries of the inverses of large positive definite Toeplitz matrices
This is an expository paper embarking on the asymptotic behavior of the entries of the inverses of positive definite symmetric Toeplitz matrices as...
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A simplified relaxed alternating positive semi-definite splitting preconditioner for saddle point problems with three-by-three block structure
For solving the saddle point linear systems with three-by-three block structure, in this paper, based on the alternating positive semi-definite...
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Cycle integrals of meromorphic modular forms and Siegel theta functions
We study meromorphic modular forms associated with positive definite binary quadratic forms and their cycle integrals along closed geodesics in the...
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On Dirichlet-integrable solutions of left-definite Hamiltonian systems
This paper aims to share a method to handle left-definite Hamiltonian systems and to construct nested-ellipsoids related with the corresponding...
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A study of certain class of strictly positives definite functions and applications
In this paper, we present certain class of strictly positive definite functions related to the extended Hurwitz-Lerch Zeta function, digamma function...
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Semi-definite Representations for Sets of Cubics on the Two-dimensional Sphere
The compact set of homogeneous quadratic polynomials in n real variables with modulus bounded by 1 on the unit sphere is trivially semi-definite...
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Further Investigation of Positive Semi-definiteness of Fourth-order Cauchy and Hilbert Tensors
In this paper, we further investigate the positive (semi-)definiteness of even order tensors. For the fourth-order tensor, we discuss the...
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Counting square-free integers represented by binary quadratic forms of a fixed discriminant
In this article, we prove a result concerning the infinitude of square-free integers represented by a class of polynomials in two variables. More...
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Harmonic weak Maass forms and periods II
In this paper we investigate the Fourier coefficients of harmonic Maass forms of negative half-integral weight. We relate the algebraicity of these...