Dirichlet’s theorem states that if q and l are two relatively prime positive integers, there are infinitely many primes of the form l+kq. Dirichlet’s theorem is a generalized statement about prime numbers and the theory of Fourier series on the finite abelian group (Z/qZ)∗ plays an important role in the solution.

We give a method to solve generalized Fermat equations of type x 4+y4 = qz, for some prime values of q and every prime p bigger than 13. We illustrate the method by proving that there are no solutions for q = 73, 89 and 113. Math. Subject Classification: 11D41,11F11

In this paper we investigate qz/4-sets of type (O,q/4,q/2) in projective planes of order q=O(mod4). These sets arise in the investigation of regular triples with respect to a hyperoval. Combinatorial properties of these sets are given and examples in Desarguesian projective planes are constructed.

We study the distribution of spacings between squares in Z/QZ as the number of prime divisors of Q tends to infinity. In [3] Kurlberg and Rudnick proved that the spacing distribution for square free Q is Poissonian, this paper extends the result to arbitrary Q.

Institut für Theoretische Physik, Universität Innsbruck,A-6020 Innsbruck, Austria a Institut für Theoretische Physik, Universität Hannover, Hannover, Germany b Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK c H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, UK d BRIMS, Hewlett-Packard Laboratories, Stoke Gifford, Bri...

We discuss a novel iterative approach for the computation of a number of eigenvalues and eigenvectors of the generalized eigenproblem A x = ABx . Our method is based on a combination of the JacobiDavidson method and the QZ-method. For that reason we refer to the method as JDQZ. The effectiveness of the method is illustrated by a numerical example.

We study a BGG-type category of infinite-dimensional representations of H[W ], a semidirect product of the quantum torus with parameter q, built on the root lattice of a semisimple group G, and the Weyl group of G. Irreducible objects of our category turn out to be parametrized by semistable G-bundles on the elliptic curve C∗/qZ .

We discuss a novel iterative approach for the computation of a number of eigenvalues and eigenvectors of the generalized eigenprob-lem Ax = Bx. Our method is based on a combination of the Jacobi-Davidson method and the QZ-method. For that reason we refer to the method as JDQZ. The eeectiveness of the method is illustrated by a numerical example.

We calculate complete basis set (CBS) limit-extrapolated ionization potentials (IPs) and electron affinities (EA) with Slater-type sets for the molecules in GW100 database. To this end, we present two new orbital (STO) of triple-(TZ) quadruple-ζ (QZ) quality, whose polarization is adequate correlated-electron methods which contain extra diffuse functions to be able correctly EAs a positive lowe...