TL;DR: In this paper, the curvature invariants of compact hyperkahler manifolds were studied in graph-theoretical form, considering them as a special case of the curvatures invariants introduced by Rozansky and Witten.
Abstract: We express characteristic numbers of compact hyperk\"ahler manifolds in graph-theoretical form, considering them as a special case of the curvature invariants introduced by Rozansky and Witten. The appropriate graphs are generated by ``wheels'' and we use the recently proved Wheeling Theorem to give a formula for the L2 norm of the curvature of an irreducible hyperk\"ahler manifold in terms of the volume and Pontryagin numbers. The formula involves the multiplicative sequence which is the square root of the A-hat polynomial.
TL;DR: In this article, it was shown that the polynomials of Chern classes corresponding to the power series Q(z) = Γ(1 + z) -1 appears in a relation between the Chern classes of certain Calabi-Yau manifolds and the periods of their mirrors.
Abstract: In a recent paper, A Libgober showed that the multiplicative sequence {Q i (c 1 ,…,c i )} of Chern classes corresponding to the power series Q(z) = Γ(1 + z) -1 appears in a relation between the Chern classes of certain Calabi-Yau manifolds and the periods of their mirrors We show that the polynomials Q i can be expressed in terms of multiple zeta values
TL;DR: In this paper, it was shown that sequences of Davenport type or Gelfond type can be realized by dynamical systems and have the strong GELFond property, which implies that the dynamical system can be fully oscillated.
Abstract: We consider sequences of Davenport type or Gelfond type and prove that sequences of Davenport exponent larger than -multiplicative sequence, the Gelfond property implies the strong Gelfond property and that sequences realized by dynamical systems can be fully oscillating and have the Gelfond property.
TL;DR: In this article, the authors consider a sequence in which each term is obtained by multiplying both previous terms and show that it is similar to Fibonacci's sequence but with some particularities that will be proved and verified.
Abstract: The aim of this work is to consider a sequence in which each term is obtained by multiplying both previous terms. This sequence is similar to Fibonacci's sequence but with some particularities that will be proved and verified.