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published_or_final_version / Mathematics / Master / Master of Philosophy

published_or_final_version / Mathematics / Master / Master of Philosophy

published_or_final_version / Physics / Master / Master of Philosophy

We study the L-values of an elliptic curve twisted by an Artin representation. Specifically, we consider the case in which the representation factors through a false Tate curve extension of Q. First, we consider a semistable elliptic curve E; we construct an integral-valued p-adic measure which interpolates the values the L-values of an Artin twist of E, at a family of finite-order character twists. To do this, we exploit the fact that such an L-value may be written as the Rankin convolution of two Hilbert modular forms, when the representation factors through the false Tate curve extension. Recent developments in non-abelian Iwasawa theory predict certain strong congruences between these p-adic L-functions, and we shall establish weakened versions of these congruences. Next, we prove analogous results for an elliptic curve with complex multiplication; we do this using work of Hida and Tilouine on the p-adic interpolation of Hecke L-functions over a CM-field. We go on to investigate the ratio of the automorphic and motivic periods associated to E in this setting. We describe how the p-valuation of this ratio may be explicitly calculated, and use the computer package MAGMA to produce some numerical examples. We end by proving a formula for the growth of this quantity in terms of the Iwasawa invariants associated to the two-variable extension of the CM-field.

The multitude of data formats for storing river network, geometry, and flow data presents a challenge for the sharing of information both internally between software applications and externally between agencies. An analysis of existing software applications and data models used for one-dimensional hydraulic modelling of river systems was performed. The commonalities and differences between the model inputs were identified in order to determine the necessary characteristics of a common transfer language. A prototype transfer language was developed using Unified Modeling Language (UML) and implemented as an Extensible Markup Language (XML) schema. This prototype is intended to serve as a first step towards developing an international open standard to facilitate the sharing of hydraulic data. This work was performed in cooperation with the Consortium of Universities for the Advancement of Hydrologic Science, Inc. (CUAHSI) and the Open Geospatial Consortium/World Meteorological Organisation Hydrology Domain Working Group. / text

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