Computations of Vector-Valued Siegel Modular Forms

We carry out some computations of vector-valued Siegel modular forms of degree two, weight (k, 2) and level one, and highlight three experimental results: (1) we identify a rational eigenform in a three-dimensional space of cusp forms; (2) we observe that non-cuspidal eigenforms of level one are not always rational; (3) we verify a number of cases of conjectures about congruences between classical modular forms and Siegel modular forms. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. (C) 2013 Elsevier Inc. All rights reserved.

Suitability of real-time quantitative PCR to estimate the relative telomere length in European Hake (Merluccius merluccius Linnaeus, 1758)

Telomere length measurement has been proposed as a promising tool to estimate the age of individuals in natural populations. We used real-time quantitative PCR (qPCR) to measure relative telomere length in four tissues (brain, kidney, liver and muscle) of European hake (Merluccius merluccius) in different groups based upon body length an otolith age estimate. We observed a high level of inter-individual differences in the measurements of relative telomere length in hakes of similar age and body length groups. The results of qPCR analysis showed a great variability in all measures and a lack of repeatability and reproducibility with significant statistical differences in the results of the different assays. The paper discusses the technical reasons for the variability in qPCR obtained in this work and by other authors.