We construct an abundance of Hilbertian domains: Let O be a countable separably Hilbertian domain with a qoutient eld K and let e 2 be an integer. Let L be an abelian extension of K such that ford(a) j a 2 G(L=K)g is unbounded, and let O L be the integral closure of O in L. Then, for almost all 2 G(K) e , each ring between O L and L K s () is separably Hilbertian.

If K/k is a finite Galois extension of number fields with Galois group G, then the kernel of the capitulation map Clk ~ ClK of ideal class groups is isomorphic to the kernel X(H) of the transfer map H/H’ ~ A, where H = Gal(K/k), A = Gal(K/K) and K is the Hilbert class field of K. H. Suzuki proved that when G is abelian, |G| divides |X(H)|. We call a finite abelian group X a transfer kernel for ...

We describe a new algebraically completely integrable system, whose integral manifolds are co-elliptic subvarieties of Jacobian varieties. This is a multi-periodic extension of the Krichever-Treibich-Verdier system, which consists of elliptic solitons. The goal of this work is to generalize the theory of elliptic solitons, which was developed by A. Treibich and J.-L. Verdier based on earlier wo...

We explain how one can dispense with the numerical computation of approximations to the transcendental integral functions involved when computing class numbers of quadratic number fields. We therefore end up with a simpler and faster method for computing class numbers of quadratic number fields. We also explain how to end up with a simpler and faster method for computing relative class numbers ...

The string representation of the Abelian projected SU(3)-gluodynamics partition function is derived by using the path-integral duality transformation. On this basis, we also derive analogous representations for the generating functionals of correlators of gluonic field strength tensors and monopole currents, which are finally applied to the evaluation of the corresponding bilocal correlators. T...

A formula constituting the non-Abelian Stokes theorem for general semi-simple compact gauge groups is presented. The formula involves a path integral over a group space and is applicable to Wilson loop variables irrespective of the topology of loops. Some simple expressions analogous to the ’t Hooft tensor of a magnetic monopole are given for the 2-form of interest. A special property in the ca...

We formulate a complete path integral bosonization procedure for any fermionic theory in two dimensions. The classical action of the bosons in the bosonized theory is −i times the logarithm of the Jacobian of a local chiral transformation, with the boson fields as transformation parameters. Three examples, the Schwinger model, the massive Thirring model and massive non-Abelian bosonization, are...

We study the Dirac propagator dressed by an arbitrary number N of photons means a worldline approach, which makes use supersymmetric N=1 spinning particle model on line, coupled to external Abelian vector field. obtain compact off-shell master formula for tree level scattering amplitudes associated propagator. In particular, unlike in other approaches, we express fermionic degrees freedom using...

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...

In this paper, we prove that every semi-Cayley graph over a group G is quasi-abelian if and only if G is abelian.