ar X iv : 0 90 4 . 31 10 v 2 [ m at h . N T ] 3 1 Ju l 2 01 0 ON CLASSIFYING MINKOWSKIAN SUBLATTICES

ar X iv : m at h - ph / 9 90 70 23 v 1 2 8 Ju l 1 99 9 EIGENFUNCTIONS , TRANSFER MATRICES , AND ABSOLUTELY CONTINUOUS SPECTRUM OF ONE - DIMENSIONAL SCHRÖDINGER OPERATORS

In this paper, we will primarily discuss one-dimensional discrete Schrödinger operators (hu)(n) = u(n + 1) + u(n − 1) + V (n)u(n) (1.1D) on ℓ 2 (Z) (and the half-line problem, h + , on ℓ 2 ({n ∈ Z | n > 0}) ≡ ℓ 2 (Z +)) with u(0) = 0 boundary conditions. We will also discuss the continuum analog (Hu)(x) = −u ′′ (x) + V (x)u(x) (1.1C) on L 2 (R) (and its half-line problem, H + , on L 2 (0, ∞) wi...

ar X iv : m at h - ph / 0 31 10 01 v 4 3 N ov 2 00 4 Clifford Valued Differential Forms , Algebraic Spinor Fields

ar X iv : 0 90 8 . 01 53 v 1 [ m at h . G T ] 2 A ug 2 00 9 On Fibonacci knots

We show that the Conway polynomials of Fibonacci links are Fibonacci polynomials modulo 2. We deduce that, when n 6≡ 0 (mod 4) and (n, j) 6= (3, 3), the Fibonacci knot F (n) j is not a Lissajous knot. keywords: Fibonacci polynomials, Fibonacci knots, continued fractions

ar X iv : 0 90 9 . 34 42 v 2 [ m at h . N T ] 1 0 A pr 2 01 0 AN EXPLICIT HEIGHT BOUND FOR THE CLASSICAL MODULAR

For a prime l, let Φl be the classical modular polynomial, and let h(Φl) denote its logarithmic height. By specializing a theorem of Cohen, we prove that h(Φl) ≤ 6l log l + 16l + 14 √ l log l. As a corollary, we find that h(Φl) ≤ 6l log l+18l also holds. A table of h(Φl) values is provided for l ≤ 3607.

ar X iv : h ep - t h / 01 01 14 8 v 2 3 0 Ju l 2 00 1 Multidimensional Phase Space and Sunset Diagrams

We derive expressions for the phase-space of a particle of momentum p decaying into N particles, that are valid for any number of dimensions. These are the imaginary parts of so-called 'sunset' diagrams, which we also obtain. The results are given as a series of hypergeometric functions, which terminate for odd dimensions and are also well-suited for deriving the threshold behaviour.