Multiple reciprocal sums and multiple reciprocal star sums of polynomials are almost never integers
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DOI: 10.1016/j.jnt.2018.06.005
Abstract: Let $n$ and $k$ be integers such that $1\le k\le n$ and $f(x)$ be a nonzero polynomial of integer coefficients such that $f(m)\ne 0$ for any positive integer $m$. For any $k$-tuple $\vec{s}=(s_1, ..., s_k)$… read more here.
Keywords: integer; vec integers; vec vec; never integers ... See more keywords
On the behaviour of the two-dimensional Hamiltonian $-\,{\rm{\Delta }}+\lambda [\delta (\vec{x}+{\vec{x}}_{0})+\delta (\vec{x}-{\vec{x}}_{0})]$ as the distance between the two centres vanishes
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DOI: 10.1088/1402-4896/ab8f3f
Abstract: In this note we continue our analysis of the behaviour of self-adjoint Hamiltonians with a pair of identical point interactions symmetrically situated around the origin perturbing various types of "free Hamiltonians" as the distance between… read more here.
Keywords: distance; delta; vec vec; delta vec ... See more keywords