Computing special values of partial zeta functions

We discuss computation of the special values of partial zeta functions associated to totally real number fields. The main tool is the \emph{Eisenstein cocycle} $\Psi$, a group cocycle for $GL_{n} (\Z )$; the special values are computed as periods of $\Psi$, and are expressed in terms of generalized Dedekind sums. We conclude with some numerical examples for cubic and quartic fields of small discriminant.Comment: 10 p

Computation of Iwasawa Lambda invariants for imaginary quadratic fields

A method for computing the Iwasawa lambda invariants of an imaginary quadratic field is developed and used to construct a table of these invariants for discriminants up to 1,000 and primes up to 20,000

The Absolute Line Quadric and Camera Autocalibration

We introduce a geometrical object providing the same information as the absolute conic: the absolute line quadric (ALQ). After the introduction of the necessary exterior algebra and Grassmannian geometry tools, we analyze the Grassmannian of lines of P^3 from both the projective and Euclidean points of view. The exterior algebra setting allows then to introduce the ALQ as a quadric arising very naturally from the dual absolute quadric. We fully characterize the ALQ and provide clean relationships to solve the inverse problem, i.e., recovering the Euclidean structure of space from the ALQ. Finally we show how the ALQ turns out to be particularly suitable to address the Euclidean autocalibration of a set of cameras with square pixels and otherwise varying intrinsic parameters, providing new linear and non-linear algorithms for this problem. We also provide experimental results showing the good performance of the techniques

Regularization of Non-commutative SYM by Orbifolds with Discrete Torsion and SL(2,Z) Duality

We construct a nonperturbative regularization for Euclidean noncommutative supersymmetric Yang-Mills theories with four (N= (2,2)), eight (N= (4,4)) and sixteen (N= (8,8)) supercharges in two dimensions. The construction relies on orbifolds with discrete torsion, which allows noncommuting space dimensions to be generated dynamically from zero dimensional matrix model in the deconstruction limit. We also nonperturbatively prove that the twisted topological sectors of ordinary supersymmetric Yang-Mills theory are equivalent to a noncommutative field theory on the topologically trivial sector with reduced rank and quantized noncommutativity parameter. The key point of the proof is to reinterpret 't Hooft's twisted boundary condition as an orbifold with discrete torsion by lifting the lattice theory to a zero dimensional matrix theory.Comment: 36 pages, references added, minor typos fixe