Let φ be a Drinfeld module of rank 2 over the field of rational functions F = Fq(T ), with EndF̄ (φ) = Fq[T ]. Let K be a fixed imaginary quadratic field over F and d a positive integer. For each prime p of good reduction for φ, let πp(φ) be a root of the characteristic polynomial of the Frobenius endomorphism of φ over the finite field Fq[T ]/p. Let Πφ(K; d) be the number of primes p of degree ...

This paper is concerned with certain connections between the ensemble of n × n unitary matrices—specifically the characteristic function of the random variable tr(U)—and combinatorics—specifically Ulam’s problem concerning the distribution of the length of the longest increasing subsequence in permutation groups—and the appearance of Painlevé functions in the answers to apparently unrelated que...

In this paper we consider an isotropic variant of the BMO-type norm recently introduced in [6]. We prove that, when considering characteristic functions of sets, this norm is related to the perimeter. A byproduct of our analysis is a new characterization of the perimeter of sets in terms of this norm, independent of the theory of distributions.

We introduce a relative index for a pair of dissipative operators in a von Neumann algebra of finite type and prove an analog of the Birman-Schwinger principle in this setting. As an application of this result, revisiting the Birman-Krein formula in the abstract scattering theory, we represent the de la Harpe-Skandalis determinant of the characteristic function of dissipative operators in the a...

1. We say that g(n) is additive if g(mn)=g(m)+g(n) holds for every coprime pairs m, n of positive integers . If, moreover, g(p') =g(p)' for every prime power pa , then g(n) is called strongly additive . By p, pi , p2 , . . ., q, qr , q2 , . . . we denote prime numbers, c, Cl, c2i . . . are suitable positive constants . F(n) and x(n) denote the largest and the smallest prime factor of n . The sy...

Finding an optimal coalition structure is a hard problem. In order to simplify this process, it is possible to explore some characteristics of the agents organization. In this paper we propose an algorithm that deals with a particular family of games in characteristic function, but is able to search in a much smaller space by considering organizational issues such as constraints in the number o...

The scope of this paper is to present a wavelet-based technique aimed at determining the range of existence for the moments of arbitrary random variables. Our work relies on the characterization of the local Hölder regularity of the characteristic function, as an indicator of the interval bounds under interest. Our motivation stems from multifractal analysis of processes.

Test statistics for testing some hypotheses on characteristic roots of covariance matrices are presented, their asymptotic distribution is derived and a confidence interval for the proportional sum of the characteristic roots is constructed. The resulting procedures are robust against violation of the normality assumptions in the sense that they asymptotically possess chosen significance level ...

Abstract: The Koszul–Vinberg characteristic function plays a fundamental role in the theory of convex cones. We give an explicit description of the function and related integral formulas for a new class of convex cones, including homogeneous cones and cones associated with chordal (decomposable) graphs appearing in statistics. Furthermore, we discuss an application to maximum likelihood estimat...

is also a fuzzy lattice. Throughout this paper, if {λj : j ∈ J} is a collection of L-sets in X , then (∨λj)(x) = ∨{λj(x) : j ∈ J}, x ∈ X ; and (∧λj)(x)=∧{λj(x) : j ∈ J}, x ∈ X . If r ∈ L, then rX denotes the fuzzy set given by rX(x) = r for all x ∈ X ; that is, rX denotes the “constant” L-set of level r, that is, the smallest and the largest elements of LX are denoted, respectively, by 0X and 1...