ar X iv : 0 90 7 . 02 06 v 1 [ m at h . N T ] 1 J ul 2 00 9 RATIONAL NUMBERS WITH PURELY PERIODIC β - EXPANSION

ar X iv : 0 90 7 . 07 87 v 1 [ m at h . G R ] 4 J ul 2 00 9 Submonoids and rational subsets of groups with infinitely many ends

In this paper we show that the membership problems for finitely generated submonoids and for rational subsets are recursively equivalent for groups with two or more ends.

ar X iv : m at h / 06 07 13 0 v 1 [ m at h . A G ] 5 J ul 2 00 6 TWISTED LOOP GROUPS AND THEIR AFFINE FLAG VARIETIES

ar X iv : h ep - p h / 02 06 06 1 v 2 9 J un 2 00 2 B̄ 0 → π + X in the Standard Model

In this paper we investigate the possibility of studying B → π form factor using the semi-inclusive decays ¯

ar X iv : 0 90 3 . 52 40 v 1 [ m at h . N T ] 3 0 M ar 2 00 9 TRANSCENDENCE OF GENERATING FUNCTIONS WHOSE COEFFICIENTS ARE MULTIPLICATIVE

Let K be a field of characteristic 0, f : N → K be a multiplicative function, and F (z) = P n≥1 f (n)z n ∈ K[[z]] be algebraic over K(z). Then either there is a natural number k and a periodic multiplicative function χ(n) such that f (n) = n k χ(n) for all n, or f (n) is eventually zero. In particular , the generating function of a multiplicative function f : N → K is either transcendental or r...

ar X iv : m at h / 06 02 44 0 v 2 [ m at h . C A ] 9 J an 2 00 7 Completeness , special functions and uncertainty principles over q - linear grids

We derive completeness criteria for sequences of functions of the form f(xλn), where λn is the nth zero of a suitably chosen entire function. Using these criteria, we construct complete nonorthogonal systems of FourierBessel functions and their q-analogues, as well as other complete sets of qspecial functions. We discuss connections with uncertainty principles over q-linear grids and the comple...