How to Solve a Quadratic Equation In Rationals

The title alludes to a similar title of the paper [3] by Grunewald and Segal, in which it is shown how to solve a quadratic equation in integers. This latter procedure seems to be quite difficult, and the algorithm outlined in [3] is rather involved, although it is completely effective in the logical sense. 1991 Mathematics Subject Classification 11D0

Galois Properties of Division Fields of Elliptic Curves

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135234/1/blms0247.pd

Algebraic independence of values of elliptic functions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46230/1/208_2005_Article_BF01450920.pd

Estimating isogenies on elliptic curves

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46570/1/222_2005_Article_BF01231178.pd

Zero estimates on group varieties II

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46615/1/222_2005_Article_BF01388605.pd

Lattice Kinetics of Diffusion-Limited Coalescence and Annihilation with Sources

We study the 1D kinetics of diffusion-limited coalescence and annihilation with back reactions and different kinds of particle input. By considering the changes in occupation and parity of a given interval, we derive sets of hierarchical equations from which exact expressions for the lattice coverage and the particle concentration can be obtained. We compare the mean-field approximation and the continuum approximation to the exact solutions and we discuss their regime of validity.Comment: 24 pages and 3 eps figures, Revtex, accepted for publication in J. Phys.