An Explicit CM Type Norm Formula and Effective Nonvanishing of Class Group L-functions for CM Fields

We show that the central value of class group L-functions of CM fields can be expressed in terms of derivatives of real-analytic Hilbert Eisenstein series at CM points. Then, following an idea of Iwaniec and Kowalski we obtain a conditional explicit lower bound of class numbers of CM fields under a weaker assumption. Some results in the proof lead to an effective nonvanishing result for class group L-functions of general CM fields, generalizing the only known ineffective results.Comment: Some typos are corrected. To appear in the Pacific Journal of Mat

Open internet access to CATV networks: experiences from the EU

Broadband over CATV networks is flourishing in the EU and in some Member States it even has already made significant impact on the retail broadband market. Our article aims to provide an overview of the regulatory treatment of broadband over CATV under the electronic communications regulatory framework. For this purpose, we carry out a survey of the different approaches within the 27 EU Member States. Based on the comments of the European Commission within the EU consultation procedure, our observation is that open Internet access obligations upon CATV operators remains limited. --access regulation,CATV,broadband

Improving the Scalability of a Prosumer Cooperative Game with K-Means Clustering

Among the various market structures under peer-to-peer energy sharing, one model based on cooperative game theory provides clear incentives for prosumers to collaboratively schedule their energy resources. The computational complexity of this model, however, increases exponentially with the number of participants. To address this issue, this paper proposes the application of K-means clustering to the energy profiles following the grand coalition optimization. The cooperative model is run with the "clustered players" to compute their payoff allocations, which are then further distributed among the prosumers within each cluster. Case studies show that the proposed method can significantly improve the scalability of the cooperative scheme while maintaining a high level of financial incentives for the prosumers.Comment: 6 pages, 4 figures, 2 tables. Accepted to the 13th IEEE PES PowerTech Conference, 23-27 June 2019, Milano, Ital