A distribution whose normalization constant is an A-hypergeometric polynomial is called an A-hypergeometric distribution. Such a distribution is in turn a generalization of the generalized hypergeometric distribution on the contingency tables with fixed marginal sums. In this paper, we will see that an A-hypergeometric distribution with a homogeneous matrix of two rows, especially, that associa...

This paper proves a sharp lower bound for Newton polygons of L-functions of exponential sums of one-variable rational functions. Let p be a prime and let Fp be the algebraic closure of the finite field of p elements. Let f(x) be any one-variable rational function over Fp with l poles of orders d1, . . . , dl. Suppose p is coprime to d1 · · · dl. We prove that there exists a tight lower bound wh...

Partial exponential sums are a generalization of classical exponential sums which are useful, for instance, for studying the distribution of the rational points along the fibers of a morphism between varieties over a finite field. They share some properties with the classical ones: their values are also governed by a certain L-function, which is rational and whose reciprocal roots are pure Weil...

Spectral discretization methods are well established methods for the computation of characteristic roots of time-delay systems. In this paper a method is presented for computing all characteristic roots in a given right half plane. In particular, a procedure for the automatic selection of the number of discretization points is described. This procedure is grounded in the connection between a sp...

1: After identification of the algebra of exponential generating series with the shuffle algebra of ordinary formal power series, the exponential map exp! : XK[[X]] −→ 1 +XK[[X]] for the associated Lie group with multiplication given by the shuffle product is well-defined over an arbitrary field K by a result going back to Hurwitz. The main result of this paper states that exp! (and its recipro...

A local lattice point counting formula, and more generally a local Euler-Maclaurin formula follow by comparing two natural families of meromorphic functions on the dual of a rational vector space V , namely the family of exponential sums (S) and the family of exponential integrals (I) parametrized by the set of rational polytopes in V . The paper introduces the notion of an interpolator between...

This paper demonstrates the use of shape-preserving exponential interpolation in a characteristic based numerical scheme for the solution of the linear advective-diiusion equation. The results from this scheme are compared with results from a number of numerical schemes in current use using test problems in one-and two-dimensions. These test cases are used to assess the merits of using shape-pr...

A scheme to model the dependence of a solute redox potential on the supporting electrolyte is proposed, and the results are compared to experimental observations and other reported theoretical models. An improved agreement with experiment is exhibited if the effect of the supporting electrolyte on the redox potential is modeled through a concentration change induced via ion pair formation with ...

In most RLWE-based homomorphic encryption schemes the native plaintext elements are polynomials in a ring Zt[x]/(x +1), where n is a power of 2, and t an integer modulus. For performing integer or rational number arithmetic one typically uses an encoding scheme, which converts the inputs to polynomials, and allows the result of the homomorphic computation to be decoded to recover the result as ...