Let μ2∞ denote the group of 2-power roots of unity. The outer pro-2 Galois representation on the projective line minus three points has a kernel whose fixed field, Ω2, is a pro-2 extension of Q (μ2∞), unramified away from 2. The fields of 2-power torsion of elliptic curves defined over Q possessing good reduction away from 2 are also pro-2 extensions of Q (μ2∞), unramified away from 2. In this ...

We review a binary sequence based on the generalized cyclotomy of order 2 with respect to p, where p is an odd prime. Linear complexities, minimal polynomials and autocorrelation of these sequences are computed.

In previous work, we have introduced the technique of relaxed power series computations. With this technique, it is possible to solve implicit equations almost as quickly as doing the operations which occur in the implicit equation. Here almost as quickly means that we need to pay a logarithmic overhead. In this paper, we will show how to reduce this logarithmic factor in the case when the cons...

We prove that the motivic class of the classifying stack of every finite linear (or projective) reflection group is trivial in the Grothendieck ring of algebraic stacks over any field containing a primitive root of unity of degree the exponent of the group. Our proof of these geometric statements rests on a combinatorial analysis of a formula by T. Ekedahl that we interpret in terms of certain ...

The structure of the tensor product representation Vλ1(x)⊗ Vλ2(y) of Uq(ŝl2) is probed at roots of unity. A polynomial identity is derived as an outcome. Also, new bases of Vλ1(x)⊗ Vλ2(y) are established under certain conditions. Permanent mailing address

Hall-Littlewood functions indexed by rectangular partitions, specialized at primitive roots of unity, can be expressed as plethysms. We propose a combinatorial proof of this formula using A. Schilling’s bijection between ribbon tableaux and ribbon rigged configurations.

The ability to distract opponents is a key mechanic in many stealth games. Existing search-based approaches to stealth analysis, however, focus entirely on solving the non-detection problem, for which they rely on static, ahead-of-time models of guard movements that do not depend on player interaction. In this work we extend and optimize an approach based on heuristic search of stealth games to...

Abst rac t . In this paper a number of binary cyclotomic generators based on cyclotomy are described. A number of cryptographic properties of the generators are controlled. A general approach to control the linear complexity and its stability for periodic sequences over any field is shown. Two bridges between number theory and stream ciphers have been" established, and the relations between the...

We define and compare, by model-theoretical methods, some exponentiations over the quantum algebra Uq(sl2(C)), for any parameter q. We discuss two cases, according to whether the parameter q is a root of unity.

We discuss two ways that the ring of coeffients for a TQFT can be reduced if one may restrict somewhat the allowed cobordisms. When we apply both methods to a TQFT associated to SO(3) and an odd prime p, we obtain a functor from a somewhat restricted cobordism category to the category of free finitely generated modules over a ring of cyclotomic integers : Z[ζp], if p ≡ −1 (mod 4), and Z[ζ4p], i...