Generalized Weil’s Reciprocity Law and Multiplicativity Theorems

On the Kernel and the Image of the Rigid Analytic Regulator in Positive Characteristic

We will formulate and prove a certain reciprocity law relating certain residues of the differential symbol dlog2 from the K2 of a Mumford curve to the rigid analytic regulator constructed by the author in a previous paper. We will use this result to deduce some consequences on the kernel and image of the rigid analytic regulator analogous to some old conjectures of Beilinson and Bloch on the co...

Variational Principle, Uniqueness and Reciprocity Theorems in Porous Piezothermoelastic with Mass Diffusion

The basic governing equations in anisotropic elastic material under the effect of porous piezothermoelastic are presented. Biot [1], Lord & Shulman [4] and Sherief et al. [5] theories are used to develop the basic equations for porous piezothermoelastic with mass diffusion material. The variational principle, uniqueness theorem and theorem of reciprocity in this model are established under the ...

The Uniqueness and Reciprocity Theorems for Generalized Thermo-Viscoelasticity with Thermal Relaxation Times

Logarithmic functional and reciprocity laws

In this paper, we give a short survey of results related to the reciprocity laws over the field C. We announce a visual topological proof of Parshin’s multidimensional reciprocity laws over C. We introduce the logarithmic functional, whose argument is an n-dimensional cycle in the group (C∗)n+1. It generalizes the usual logarithm, which can be considered as the zero-dimensional logarithmic func...

Ehrhart-macdonald Reciprocity Extended

For a convex polytope P with rational vertices, we count the number of integer points in integral dilates of P and its interior. The Ehrhart-Macdonald reciprocity law gives an intimate relation between these two counting functions. A similar counting function and reciprocity law exists for the sum of all solid angles at integer points in dilates of P . We derive a unifying generalization of the...