Related papers: Evaluating Whittaker functions and Maass forms for…
Squared eigenfunctions are quadratic combinations of Jost functions and adjoint Jost functions which satisfy the linearized equation of an integrable equation. In this article, squared eigenfunctions are derived for the Sasa-Satsuma…
A mapping M(t) is considered to obtain some preliminary results and a new trapezoidal form of Fejer inequality related to the h-convex functions. Furthermore the obtained results are applied to achieve some new inequalities in connection…
We present a new exact algorithm for estimating all elements of the quark propagator. The advantage of the method is that the exact all-to-all propagator is reproduced in a large but finite number of inversions. The efficacy of the…
The paper discusses some properties of the modulus $|W_{k,m}(z)|$ of the Whittaker function $W_{k,m}(z)$. In particular, completely monotone functions expressed in terms of $|W_{k,m}(z)|$ are found. The results follow from an integral…
We study a Lax pair in a $2$-parameter Lie algebra in various representations. The overlap coefficients of the eigenfunctions of $L$ and the standard basis are given in terms of orthogonal polynomials and orthogonal functions. Moreover,…
We study some aspects of the ${\cal O}(a)$ improved Sheikholeslami-Wohlert (SW) action for the lattice Schwinger model. We find some improvement concerning the distribution of eigenvalues of the Dirac operator and of the masses but little…
In this article we study properties of Ramanujan's mock theta functions that can be expressed in Lerch sums. We mainly show that each Lerch sum is actually the integral of a Jacobian theta function (here we show that for $\vartheta_3(t,q)$…
In this article we give a unified treatment of the construction of all possible Weitzenb\"ock formulas for all irreducible, non--symmetric holonomy groups. The resulting classification is two--fold, we construct explicitly a basis of the…
We present some properties of the Weierstrass $\wp$-function associated to the hexagonal (or triangular) lattice. In particular, with the help of an old theorem of I.N. Baker \cite{B} on the characterization of meromorphic solutions of the…
The knowledge of the exact structure of the optical system PSF enables a high-quality image reconstruction in fluorescence microscopy. Accurate PSF models account for the vector nature of light and the phase and amplitude modifications.…
The purpose of this paper is to collect and make explicit the results of Langlands, Bump, Miyazaki and Manabe, Ishii and Oda for the $GL(3)$ Eisenstein series and Whittaker functions which are non-trivial on $SO(3,\mathbb{R})$. The final…
In this paper, we use a regularized theta lifting to construct harmonic Maass forms corresponding to binary theta functions of weight $k \ge 2$ under the $\xi$-operator. As a result, we show that their holomorphic parts have algebraic…
An algorithm for computing an analytic function of a matrix $A$ is described. The algorithm is intended for the case where $A$ has some close eigenvalues, and clusters (subsets) of close eigenvalues are separated from each other. This…
We give explicit formulas for Whittaker functions for the class one principal series representations of the orthogonal groups $ SO_{2n+1}(\R) $ of odd degree. Our formulas are similar to the recursive formulas for Whittaker functions on…
We prove a weak-type (1, 1) inequality involving conditioned versions of square functions for martingales in noncommutative $L^p$-spaces associated with finite von Neumann algebras. As application, we determine the optimal orders for the…
An algorithm to compute Dirichlet $L$-functions for many quadratic characters is derived. The algorithm is optimal (up to logarithmic factors) provided that the conductors of the characters under consideration span a dyadic window.
The eigenvalue problem is a fundamental problem in scientific computing. In this paper, we first give the error analysis for a single step or sweep of Jacobi's method in floating point arithmetic. Then we propose a mixed precision…
In this paper, we explicitly construct harmonic Maass forms that map to the weight one theta series associated by Hecke to odd ray class group characters of real quadratic fields. From this construction, we give precise arithmetic…
We investigate a new model for the finite one-dimensional quantum oscillator based upon the Lie superalgebra sl(2|1). In this setting, it is natural to present the position and momentum operators of the oscillator as odd elements of the Lie…
A new method for continuing the usual Dirichlet series that defines the Riemann zeta function ${\zeta}(s)$ is presented. Numerical experiments demonstrating the computational efficacy of the resulting continuation are discussed.