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We introduce a geometric analog of the Hilbert symbol and show a Hilbert type reciprocity law for a 3-dimensional foliated dynamical system (FDS3 for short). This answers the question posed by Deninger. For this, we employ the theory of smooth Deligne cohomology and the integration theory of Deligne cohomology classes. We also present a structure theorem for an FDS3, which yields a classification of FDS3's, and we construct concrete examples of FDS3's for each type of the classification. [ABSTRACT FROM AUTHOR]

We study the twisted knot module for the universal deformation of an SL2-representation of a knot group and introduce an associated L-function, which may be seen as an analogue of the algebraic p-adic L-function associated to the Selmer module for the universal deformation of a Galois representation. We then investigate two problems proposed by Mazur: Firstly we show the torsion property of the twisted knot module over the universal deformation ring under certain conditions. Secondly we compute the L-function by some concrete examples for 2-bridge knots. [ABSTRACT FROM AUTHOR]