AbstractWe define a p-adic character to be a continuous homomorphism from For p > 2, we use the ring of big Witt vectors over to exhibit a bijection between p-adic characters and sequences (ci)(i,p)=1 of elements in indexed by natural numbers relatively prime to p, and for which . To such a p-adic character we associate an L-function, and we prove that this L-function is p-adic meromorphic if the corresponding sequence (ci) is overconvergent. If more generally the sequence is C log-convergent, we show that the associated L-function is meromorphic in the open disk of radius qC. Finally, we exhibit examples of C log-convergent sequences with associated L-functions which are not meromorphic in the disk of radius qC+∊ for any ∊ > 0.

Our analytics challenge is is to identify, characterize, and visualize anomalous subsets of large collections of network connection data. We use a combination of HPC resources, advanced algorithms, and visualization techniques. To effectively and efficiently identify the salient portions of the data, we rely on a multi-stage workflow that includes data acquisition, summarization (feature extraction), novelty detection, and classification. Once these subsets of interest have been identified and automatically characterized, we use a state-of-the-art high-dimensional query system to extract data subsets for interactive visualization. Our approach is equally useful for other large-data analysis problems where it is more practical to identify interesting subsets of the data for visualization than to render all data elements. By reducing the size of the rendering workload, we enable highly interactive and useful visualizations. As a result of this work we were able to analyze six months worth of data interactively with response times two orders of magnitude shorter than with conventional methods.

The Cryogenic Underground Observatory for Rare Events (CUORE) is the first bolometric experiment searching for neutrinoless double beta decay that has been able to reach the 1-ton scale. The detector consists of an array of 988 TeO 2 crystals arranged in a cylindrical compact structure of 19 towers, each of them made of 52 crystals. The construction of the experiment was completed in August 2016 and the data taking started in spring 2017 after a period of commissioning and tests. In this work we present the neutrinoless double beta decay results of CUORE from examining a total TeO 2 exposure of 86.3 kg yr , characterized by an effective energy resolution of 7.7 keV FWHM and a background in the region of interest of 0.014 counts / ( keV kg yr ) . In this physics run, CUORE placed a lower limit on the decay half-life of neutrinoless double beta decay of 130 Te > 1.3 · 10 25 yr (90% C.L.). Moreover, an analysis of the background of the experiment is presented as well as the measurement of the 130 Te 2 ν β β decay with a resulting half-life of T 1 / 2 2 ν = [ 7.9 ± 0.1 ( stat . ) ± 0.2 ( syst . ) ] × 10 20 yr which is the most precise measurement of the half-life and compatible with previous results.