We show that the set of colored Jones polynomials and the set of generalized Alexander polynomials defined by Akutsu, Deguchi and Ohtsuki intersect non-trivially. Moreover it is shown that the intersection is (at least includes) the set of Kashaev’s quantum dilogarithm invariants for links. Therefore Kashaev’s conjecture can be restated as follows: The colored Jones polynomials determine the hy...

Tate and Voloch have conjectured that the p-adic distance from torsion points of semi-abelian varieties over Cp to subvarieties may be uniformly bounded. We prove this conjecture for torsion points on semi-abelian varieties over Qp using methods of algebraic model theory and a result of Sen on Galois representation of Hodge-Tate type. As a generalization of their theorem on linear forms in p-ad...

Let p be an odd prime and F a field of characteristic different from p containing a primitive p\h root of unity. Assume that the Galois group G of the maximal p-extension of F has a finite normal series with abelian factor groups. Then the commutator subgroup of G is abelian. Moreover, G has a normal abelian subgroup with pro-cyclic factor group. If, in addition, F contains a primitive p2th roo...

The lattice of intersections of reflecting hyperplanes of a complex reflection group W may be considered as the poset of 1-eigenspaces of the elements of W . In this paper we replace 1 with an arbitrary eigenvalue and study the topology and homology representation of the resulting poset. After posing the main question of whether this poset is shellable, we show that all its upper intervals are ...

LetX denote the rational curve with n+1 nodes obtained from the Riemann sphere by identifying 0 with∞ and ζj with −ζj for j = 0, 1, . . . , n−1, where ζ is a primitive (2n)th root of unity. We show that if n is even, then X has no smooth Weierstrass points, while if n is odd, then X has 2n smooth Weierstrass points. C. Widland [14] showed that the rational curve with three nodes obtained from P...

meaning of islamic unity in two internal & external levels of diplomatic idea of islam has superior place. present situation of world of islam and various devilish plots for provoking disputes and enmity among the muslims shows well the necessity of this issue. undoubtedly, the survey of valuable experience of leaders of islamic world unity at present age, especially survey of seyed jamal al-di...

Concentration and equi-distribution, near the unit circle, in Solomyak’s set, of the union of the Galois conjugates and the beta-conjugates of a Parry number β are characterized by means of the Erdős-Turán approach, and its improvements by Mignotte and Amoroso, applied to the analytical function fβ(z) = −1 + ∑ i≥1 tiz i associated with the Rényi β-expansion dβ(1) = 0.t1t2 . . . of unity. Mignot...

when belief priniplees among all muslems became identi cal, this opportunity has bee provided for clergyman scientist to infere legal command ments to rely it, that it lead to emergence of prudence religion and diversity of opinions. although this practice religious leads to dispute about opinions, but they are not related to beliefe principles. thus it isn't worthy that these disputes don...

We prove that the SU.(2) Witten-Reshetikhin-Turaev invariant of any 3-manifold with any colored link inside at any root of unity is an algebraic integer. As a byproduct, we get a new proof of the integrality of the SO.(3) Witten-Reshetikhin-Turaev invariant for any 3-manifold with any colored link inside at any root of unity of odd order. DOI: https://doi.org/10.4171/QT/48 Posted at the Zurich ...