We characterize the space of the so-called planar mixed automorphic forms of type (ν, μ) with respect to an equivariant pair (ρ, τ) as the image of the usual automorphic forms by an appropriate transform and we investigate some concrete basic spectral properties of a magnetic Schrödinger operator acting on them. The associated polynomials constitute classes of generalized complex polynomials of...

The perfect Golay codes lifted over the finite rings Z2m and Z3m, or over their infinite counterparts, namely the 2-adic and 3-adic rings, are considered, and their algebraic decoding is obtained as a non-trivial extension of the algebraic decoding of the perfect Golay codes. Mathematics Subject Classification: 94B15, 94B35, 11D88, 14G50

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

We study special values of Carlitz’s q-Fibonacci and q-Lucas polynomials Fn(q, t) and Ln(q, t). Brief algebraic and detailed combinatorial treatments are presented, the latter based on the fact that these polynomials are bivariate generating functions for a pair of statistics defined, respectively, on linear and circular domino arrangements.

Using Casorati determinants of Meixner polynomials (m n )n , we construct for each pair F = (F1, F2) of finite sets of positive integers a sequence of polynomials ma,c;F n , n ∈ σF , which are eigenfunctions of a second order difference operator, where σF is certain infinite set of nonnegative integers, σF N. When c and F satisfy a suitable admissibility condition, we prove that the polynomials...