We study mock and mixed mock modular forms in the lower half-plane. In particular, our results apply to Zwegers’ three-variable mock Jacobi form μ(u, v; τ), three-variable generalizations of the universal mock modular partition rank generating function, and the quantum and mock modular strongly unimodal sequence rank generating function. We do not rely upon the analytic properties of these func...

Polynomial matrices G(z) = Izm−Cizi with hermitian coefficients Ci are studied. The assumption ∑ |Ci| I implies that the characteristic values of G(z) lie in the closed unit disc. The characteristic values of modulus one are roots of unity. An extension of the Eneström– Kakeya theorem is proved and a stability criterion for a system of difference equations is given. Mathematics subject classifi...

Let p be prime, K a field of characteristic 0. Let (x1, . . . , xn) ∈ Kn such that xi 6= 0 for all i and xi/xj is not a root of unity for all i 6= j. We prove that there exist integers 0 < e1 < e2 < · · · < en such that det (x ei j ) 6= 0. The proof uses p-adic arguments. As corollaries, we derive the linear independence of certain Witt vectors and study the result of applying the Witt functor ...

Properties of the simplest class of self-similar potentials are analyzed. Wave functions of the corresponding Schrödinger equation provide bases of representations of the q-deformed Heisenberg-Weyl algebra. When the parameter q is a root of unity the functional form of the potentials can be found explicitly. The general q3 = 1 and the particular q4 = 1 potentials are given by the equianharmonic...

For a connected, semisimple, simply connected algebraic group G defined and isotropic over a field k, the corresponding Tits building is used to study central extensions of the abstract group G(k). When k is a nonArchimedean local field and A is a finite, abelian p-group where p is the characteristic of the residue field of k, then with G of k-rank at least 2, we show that the group H2(G(k), A)...

All indecomposable unimodular hermitian lattices in dimensions 14 and 15 over the ring of integers in Q( √ −3) are determined. Precisely one lattice in dimension 14 and two lattices in dimension 15 have minimal norm 3. In 1978 W. Feit [10] classified the unimodular hermitian lattices of dimensions up to 12 over the ring Z[ω] of Eisenstein integers, where ω is a primitive third root of unity. Th...