Introduction. Suppose that G is a reductive algebraic group defined over Q. There occurs in the trace formula a remarkable distribution on G(A)l which is supported on the unipotent set. It is defined quite concretely in terms of a certain integral over G(Q)\G(A)1. Despite its explicit description, however, this distribution is not easily expressed locally, in terms of integrals on the groups G(...

We construct a commutative algebra Ax of difference operators in R, depending on p + 3 parameters which is diagonalized by the multivariable Racah polynomials Rp(n; x) considered by Tratnik [27]. It is shown that for specific values of the variables x = (x1, x2, . . . , xp) there is a hidden duality between n and x. Analytic continuation allows us to construct another commutative algebra An in ...

The concept of permutograph is introduced and properties of integral functions on permutographs are established. The central result characterizes the class of integral functions that are representable as lattice polynomials. This result is used to establish lattice polynomial representations of piecewise linear functions on R and continuous selectors on linear orders.

Subdividable linear efficient function enclosures (Slefes) provide, at low cost, a piecewise linear pair of upper and lower bounds f, f, that sandwich a function f on a given interval: f ≥ f ≥ f. In practice, these bounds are observed to be very tight. This paper addresses the question just how close to optimal, in the max-norm, the slefe construction actually is. Specifically, we compare the w...

the coefficients of the two po1,ynomials are known, they can be used to generate thle parameter over the entire band of interest. The principle analytic continuation is used to generate broadband information from narrow band lized to generate broadband currents on a body from points or measured data. The given data, as a funcwhich its Radar Cross Section (RCS) is calculated. tion of frequency, ...

indicates the term corresponding to j = h is to be deleted. If one of the a, = 0 or a negative integer, then (1) always converges, since it terminates. Otherwise it converges for all finite x if P ^ Q and for |a;| < 1 if P = Q + 1. In this case, however, the function can be analytically continued into the cut plane |arg (1 — a;)| < x, and we shall often denote by q+iFq(x) not only the series (1...

This article, a continuation of [HRo], constructs the Satake parameter for any irreducible smooth J-spherical representation of a p-adic group, where J is any parahoric subgroup. This parametrizes such representations when J is a special maximal parahoric subgroup. The main novelty is for groups which are not quasi-split, and the construction should play a role in formulating a geometric Satake...

We use a variant of a method of Goncharov, Kontsevich, and Zhao [Go2, Z] to meromorphically continue the multiple Hurwitz zeta function ζd(s; θ) = ∑ 0<n1<···<nd (n1 + θ1) −s1 · · · (nd + θd)d , θk ∈ [0, 1), to C, to locate the hyperplanes containing its possible poles, and to compute the residues at the poles. We explain how to use the residues to locate trivial zeros of ζd(s; θ).

In an irreducible stochastic game, no single player can prevent the stochastic process on states from being irreducible, so the other players can ensure that the current state has little effect on events in the distant future. This paper provides a sufficient condition for the folk theorem in irreducible stochastic games with imperfect public monitoring, thus generalizing the folk theorems of D...

Given a projective variety X defined over a finite field, the zeta function of divisors counts all irreducible, codimension one subvarieties of X, each measured by their projective degree. For dim(X) ≥ 2, this is a purely p-adic function. Four conjectures are expected to hold, the first of which is p-adic meromorphic continuation to the all of Cp. When the divisor class group of X has rank one,...