On the minimal ramification problem for ℓ\ell-groups

Let p be a prime number. It is not known if every finite p-group of rank n>1 can be realized as a Galois group over Q with no more than n ramified primes. We prove that this can be done for the family of finite p-groups which contains all the cyclic groups of p-power order, and is closed under direct products, wreath products, and rank preserving homomorphic images. This family contains the Sylow p-subgroups of the symmetric groups and of the classical groups over finite fields of characteristic not p. On the other hand, it does not contain all finite p-groups.Comment: 8 pages. Note added at the en

Determining L-functions by twists

AbstractSuppose that L1(s) and L2(s) are two L-functions whose twists by a set of Dirichlet characters simultaneously vanish (vanish mod p) at a critical point. We examine the extent to which this property determines the L-functions in the cases of L-functions of elliptic curves, of number fields, and of curves over finite fields

Community Democratization of Telecommunications Community Cooperatives in Argentina: The Case Of TELPIN

A telecommunications community cooperative (TCC) is an autonomous association of individuals, which join forces to solve common economic, social, and cultural needs and aspirations through a jointly owned enterprise, democratically governed and managed. In Argentina, TCCs were created by community conscious members to fill in for the State role when it was unable to provide telephone service in remote areas, generally marginalized from services provision. In 1989, the State telephone enterprise was privatized. From 1992 onwards, TCCs replaced the large private telephone enterprises, since these were not interested in providing non profitable services in remote or low-populated areas. TCCs provide telephone and Internet services, by dial-up and/or broadband (ADSL) connections, as well as IP telephony, to their target populations at significantly lower costs than the large traditional firms (Telefónica and Telecom). Most of them offer also free community services, such as courses on information and communication technologies (ICTs), free Internet access to public schools, libraries, and public facilities (police stations, hospitals, etc.). This work focuses on a particular case study: TELPIN, the Pinamar Telecommunications Cooperative. Telpin was created by a group of Pinamar neighbors, most of them founders of the local community, in 1962. Since then, it has become the largest and most successful Telecommunications Cooperative in Argentina

Big Biases Amongst Products of Two Primes

We show that substantially more than a quarter of the odd integers of the form pqpq up to xx, with p,qp,q both prime, satisfy p≡q≡3 (mod4)p≡q≡3 (mod4)