Shintani cocycles and vanishing order of pp-adic Hecke LL-series at s=0s=0

Let $\chi$ be a Hecke character of finite order of a totally real number field $F$. By using Hill's Shintani cocyle we provide a cohomological construction of the $p$-adic $L$-series $L_p(\chi, s)$ associated to $\chi$. This is used to show that $L_p(\chi, s)$ has a trivial zero at $s=0$ of order at least equal to the number of places of $F$ above $p$ where the local component of $\chi$ is trivial

On special zeros of pp-adic LL-functions of Hilbert modular forms

Let $E$ be a modular elliptic curve over a totally real number field $F$. We prove the weak exceptional zero conjecture which links a (higher) derivative of the $p$-adic $L$-function attached to $E$ to certain $p$-adic periods attached to the corresponding Hilbert modular form at the places above $p$ where $E$ has split multiplicative reduction. Under some mild restrictions on $p$ and the conductor of $E$ we deduce the exceptional zero conjecture in the strong form (i.e.\ where the automorphic $p$-adic periods are replaced by the \cL-invariants of $E$ defined in terms of Tate periods) from a special case proved earlier by Mok. Crucial for our method is a new construction of the $p$-adic $L$-function of $E$ in terms of local data

Solution of a uniqueness problem in the discrete tomography of algebraic Delone sets

We consider algebraic Delone sets $\varLambda$ in the Euclidean plane and address the problem of distinguishing convex subsets of $\varLambda$ by X-rays in prescribed $\varLambda$-directions, i.e., directions parallel to nonzero interpoint vectors of $\varLambda$. Here, an X-ray in direction $u$ of a finite set gives the number of points in the set on each line parallel to $u$. It is shown that for any algebraic Delone set $\varLambda$ there are four prescribed $\varLambda$-directions such that any two convex subsets of $\varLambda$ can be distinguished by the corresponding X-rays. We further prove the existence of a natural number $c_{\varLambda}$ such that any two convex subsets of $\varLambda$ can be distinguished by their X-rays in any set of $c_{\varLambda}$ prescribed $\varLambda$-directions. In particular, this extends a well-known result of Gardner and Gritzmann on the corresponding problem for planar lattices to nonperiodic cases that are relevant in quasicrystallography.Comment: 21 pages, 1 figur

Improvements and Future Challenges for the Research Infrastructure in the Field of “Preschool Education”

Given the importance of the early stage of a child`s life and taking into account that there various initiatives underway to improve preschool programs in German, it is remarkable that there are only a few microdatasets covering the field of preschool education in Germany - even less if the focus is on nationally representative datasets. The majority of these at least provide information on attendance of preschool programs. In principle there are two main groups of data: data that comprise part of the official statistics and survey data. However, there are hardly any data which allow a linkage between preschool program information and child outcome data. Furthermore, better data for children up to three years are needed, as well as data for children from migrant families. In particular, there is a need for good panel data allowing to match individual data and institutional information Given the developments in the German data infrastructure, the potentials for preschool education research will certainly improve. Nevertheless there remain a number of gaps. Among the mentioned recommendations the paper recommend improvements in fields, such as better data on the quality of preschool programs, better data on the family context and the costs of preschool education and finally the paper addresses the need for detailed intervention studies (on a representative (generalizable) level, which help to learn more about the most effective and efficient parameters of preschool programs.preschool education, day care, child outcomes

Geodetic measurements at sea floor spreading centers

A network of 8 or more precision transponder units mounted on the sea floor and interrogated periodically from an instrument package towed near bottom through the area to provide the necessary spatial averaging could provide a practical system for observing the pattern of buildup of strain at intermediate and fast spreading centers