We view an algebraic curve over Q as providing a one-parameter family of number fields and obtain bounds for the average value of some standard prime ideal counting functions over these families which are better than averaging the standard estimates for these functions. 2000 Mathematics Subject Classification: 11R44

Résumé : Frequent and closed patterns are at the core of numerous Knowledge Discovery processes. Their mining is known to be difficult, because of the huge size of the search space, exponentially growing with the number of attributes. Unfortunately, most studies about pattern mining do not address the difficulty of the task, and provide their own algorithm. In this paper, we propose some new re...

This paper presents a new tool for the study of relationships between total path length or average depth and number of misclafficiations for decision trees. In addition to algorithm, the paper also presents the results of experiments with datasets from UCI ML Repository [1].

A repetition is an important property of a string. In this paper we consider the average number of occurrences of primitively rooted repetitions in necklace. First, we define circular square and circular run for a string and show the average number of them. Using these results, we obtain the average number of squares, the average number of runs and the average sum of exponents of runs in a neck...

In communication networks, ”vulnerability” indicates the resistance of a network to disruptions in communication after a breakdown of some processors or communication links. We may use graphs to model networks, as graph theoretical parameters can be used to describe the stability and reliability of communication networks If we think of a graph as modeling a network, the average lower independen...

We let φ(·) and τ(·) denote the Euler function and the number-ofdivisors function, respectively. In this paper, we study the average value of τ(φ(n)) when n ranges in the interval [1, x].

Number-theoretic rules are particularly suited for the approximation of multi-dimensional integrals in which the integrands are periodic. When the integrands are not periodic, then a vertex-modiied variant has been proposed. An error bound for such vertex-modiied rules is based on a simple generalization of the L2 discrepancy. In s dimensions these vertex-modiied rules contain 2 s weights which...

λf (p) = Tr(ρ(Frobp)) χ(p) = det(ρ(Frobp)) for all p not dividing N . Following [4], we define SArtin 1/4,k (N,χ) to be the finite set of primitive weight k cupsidal eigenforms which admit an associated Galois representation. If ρ : Gal(Q̄/Q)→ GL2(C) is a Galois representation, we define Pρ to be the composition of ρ with the natural projection GL2(C)→ PGL2(C). Two-dimensional complex Galois rep...

In a communication network, several vulnerability measures are used to determine the resistance of the network to disruption of operation after the failure of certain stations or communication links. If the communication network is modeled as a simple, undirected, connected and unweighted graph G, then average lower independence number of a graph G can be considered as a measure of graph vulner...

The upper bound and the lower bound of average numbers of divisors of Euler Phi function and Carmichael Lambda function are obtained by Luca and Pomerance (see [LP]). We improve the lower bound and provide a heuristic argument which suggests that the upper bound given by [LP] is indeed close to the truth.