Showing papers in "Canadian Mathematical Bulletin in 2006"
TL;DR: In this article, the authors give a characterization of products of projective spaces using unsplit covering families of rational curves, and show that the product can be characterized using rational curves.
Abstract: We give a characterization of products of projective spaces using unsplit covering families of rational curves.
46 citations
TL;DR: In this paper, the weight functions on such that where where is the norm of the associate space to the space determined by the norm where where where the norm is the weight norm.
Abstract: We characterize the weight functions on such that where As an application we present a new simple characterization of the associate space to the space , determined by the norm where
38 citations
TL;DR: In this paper, the vanishing Lie derivative of the shape operator along the direction of the Reeb vector field was used to characterize real hypersurfaces of type A in a complex two-plane Grassmannian G2(C m+2 ) which are tubes over totally geodesic G 2(Cm+1 ) in G2m+2 ).
Abstract: In this paper we give a characterization of real hypersurfaces of type A in a complex two- plane Grassmannian G2(C m+2 ) which are tubes over totally geodesic G2(C m+1 ) in G2(C m+2 ) in terms of the vanishing Lie derivative of the shape operator A along the direction of the Reeb vector field �.
31 citations
TL;DR: In this article, it was shown that any set of cofibrations containing the standard set of generating projective co-ibrations determines a co-fibrantly generated proper closed model structure on the category of simplicial presheaves on a small Grothendieck site.
Abstract: Abstract This note shows that any set of cofibrations containing the standard set of generating projective cofibrations determines a cofibrantly generated proper closed model structure on the category of simplicial presheaves on a small Grothendieck site, for which the weak equivalences are the local weak equivalences in the usual sense.
28 citations
TL;DR: In this paper, an explicit formula for the non-abelian twisted sign-determined Reidemeister torsion of a fibered knot in terms of its monodromy was given.
Abstract: In this article, we give an explicit formula to compute the non-abelian twisted sign-determined Reidemeister torsion of the exterior of a fibered knot in terms of its monodromy. As an application, we give explicit formulae for the non abelian Reidemeister torsion of torus knots and of the figure eight knot.
27 citations
TL;DR: In this article, the modularity of three nonrigid Calabi-Yau threefolds with bad reduction at 11 was investigated, and they were constructed as fibre products of rational elliptic sur- faces, involving the modular elliptic surface of level 5.
Abstract: This paper investigates the modularity of three non-rigid Calabi-Yau threefolds with bad reduction at 11. They are constructed as fibre products of rational elliptic sur- faces, involving the modular elliptic surface of level 5. Their middle l-adic cohomology groups are shown to split into two-dimensional pieces, all but one of which can be inter- preted in terms of elliptic curves. The remaining pieces are associated to newforms of weight 4 and level 22 or 55, respectively. For this purpose, we develop a method by Serre to compare the corresponding two-dimensional 2-adic Galois representations with uneven trace. Eventually this method is also applied to a self fibre product of the Hesse-pencil, relating it to a newform of weight 4 and level 27.
26 citations
TL;DR: In this article, the authors study sequences of integers for which the second differences between their squares are constant and show that there are infinitely many monotone sextuples having this property and discuss some related problems.
Abstract: The aim of this paper is to study sequences of integers for which the second differences between their squares are constant. We show that there are infinitely many nontrivial monotone sextuples having this property and discuss some related problems.
25 citations
TL;DR: In this article, it was shown that a skew-symmetric self-reciprocal Littlewood polynomial cannot have any zeros on the unit circle, as well as providing a new proof of the known result.
Abstract: We call �(z) = a0 + a1z + � � � + an 1z n 1 a Littlewood polynomial if a j = ±1 for all j. We call �(z) self-reciprocal if �(z) = z n 1 �(1/z), and call �(z) skewsymmetric if n = 2m + 1 and am+ j = (−1) j am j for all j. It has been observed that Littlewood polynomials with particularly high minimum modulus on the unit circle in C tend to be skewsymmetric. In this paper, we prove that a skewsymmetric Littlewood polynomial cannot have any zeros on the unit circle, as well as providing a new proof of the known result that a self-reciprocal Littlewood polynomial must have a zero on the unit circle.
25 citations
TL;DR: In this paper, the structure of the full lift for the Howe correspondence of for rank-one reducibilities was determined, and the structure was shown to be the same as in this paper.
Abstract: In this paper we determine the structure of the full lift for the Howe correspondence of for rank-one reducibilities.
21 citations
TL;DR: For a class of Blaschke products with zeros in a Stolz angle, it was shown in this article that the Bergman spaces with zero sequences are equivalent to the membership of in the space.
Abstract: It is known that the derivative of a Blaschke product whose zero sequence lies in a Stolz angle belongs to all the Bergman spaces with . The question of whether this result is best possible remained open. In this paper, for a large class of Blaschke products with zeros in a Stolz angle, we obtain a number of conditions which are equivalent to the membership of in the space . As a consequence, we prove that there exists a Blaschke product with zeros on a radius such that .
15 citations
TL;DR: In this article, the authors studied the Lp mapping properties of a class of singular integral operators with rough kernels belonging to certain block spaces and proved that their operators are bounded on Lp provided that their kernels satisfy a size condition much weaker than that for the classical Calder´ on-Zygmund singular integral operator.
Abstract: In this paper, we study the Lp mapping properties of a class of singular integral operators with rough kernels belonging to certain block spaces. We prove that our operators are bounded on Lp provided that their kernels satisfy a size condition much weaker than that for the classical Calder´ on- Zygmund singular integral operators. Moreover, we present an example showing that our size condi- tion is optimal. As a consequence of our results, we substantially improve a previously known result on certain maximal functions.
TL;DR: In this paper, the Cayley-Dickson process is applied to the division algebra of real octonions and a 16-dimensional real algebra known as (real) sedenions.
Abstract: By applying the Cayley-Dickson process to the division algebra of real octonions, one ob- tains a 16-dimensional real algebra known as (real) sedenions. We denote this algebra by A4. It is a flexible quadratic algebra (with unit element 1) but not a division algebra. We classify the subalgebrasof A4 up to conjugacy(i.e., up to the action of the automorphismgroup G of A4) with one exception: we leave aside the more complicated case of classifying the quaternion subalgebras. Any nonzero subalgebra contains 1 and we show that there are no proper subalgebras of dimension 5, 7 or > 8. The proper non-division subalgebras have dimensions 3, 6 and 8. We show that in each of these dimensions there is exactly one conjugacy class of such subalgebras. There are infinitely many conjugacy classes of subalgebras in dimensions 2 and 4, but only 4 conjugacy classes in dimension 8.
TL;DR: In this article, it was shown that end RM is clean for any semisimple module M over an arbitrary ring R provided that g(x) ∈ (x − a)(x − b)C(x), where a, b ∈ C and both b and b − a are units in R.
Abstract: If C = C(R) denotes the center of a ring R and g(x) is a polynomial in C(x), Camillo and Sim´ on called a ring g(x)-clean if every element is the sum of a unit and a root of g(x). If V is a vector space of countable dimension over a division ring D, they showed that end DV is g(x)-clean provided that g(x) has two roots in C(D). If g(x) = x − x 2 this shows that end DV is clean, a result of Nicholson and Varadarajan. In this paper we remove the countable condition, and in fact prove that end RM is g(x)-clean for any semisimple module M over an arbitrary ring R provided that g(x) ∈ (x − a)(x − b)C(x) where a, b ∈ C and both b and b − a are units in R.
TL;DR: In this article, a Bernstein-Walsh type inequality for functions of several variables is derived, which then is applied to obtain analogs and generalizations of the following classical theorems: Bochnak-Siciak theorem, Zorn-Lelong theorem, Abhyankar-Moh-Sathaye theorem, and the transfinite diameter of the convergence set of a divergent series.
Abstract: A Bernstein–Walsh type inequality for functions of several variables is derived, which then is applied to obtain analogs and generalizations of the following classical theorems: (1) Bochnak– Siciak theorem: a function on that is real analytic on every line is real analytic; (2) Zorn–Lelong theorem: if a double power series converges on a set of lines of positive capacity then is convergent; (3) Abhyankar–Moh–Sathaye theorem: the transfinite diameter of the convergence set of a divergent series is zero.
TL;DR: In this paper, it was shown that given a stable weighted configuration on the asymptotic boundary of a compact Hadamard space, there is a polygon with Gauss map prescribed by the given weighted configuration.
Abstract: We show that given a stable weighted configuration on the asymptotic boundary of a lo- cally compact Hadamard space, there is a polygon with Gauss map prescribed by the given weighted configuration. Moreover, the same result holds for semistable configurations on arbitrary Euclidean buildings.
TL;DR: In this article, the authors extended the methods of Van der Poorten and Chapman for explicitly evaluating the Dedekind eta function at quadratic irrationalities with class numbers 3 and 4.
Abstract: We extend the methods of Van der Poorten and Chapman for explicitly evaluating the Dedekind eta function at quadratic irrationalities. Via evaluation of Hecke -series we obtain new evaluations at points in imaginary quadratic number fields with class numbers 3 and 4. Further, we overcome the limitations of the earlier methods and via modular equations provide explicit evaluations where the class number is 5 or 7.
TL;DR: In this paper, the authors consider the case in which the dual action of the quotient group is free almost everywhere and derive a Hausdorff-young inequality for non-unimodular groups.
Abstract: This paper studies Hausdorff–Young inequalities for certain group extensions, by use of Mackey's theory. We consider the case in which the dual action of the quotient group is free almost everywhere. This result applies in particular to yield a Hausdorff–Young inequality for nonunimodular groups.
TL;DR: In this paper, a free analogization of the logarithmic Sobolev inequality is obtained for measures on the circle, based on a random matrix approximation procedure, and a large deviation result concerning the eigenvalue distribution of special unitary matrices is applied and discussed.
Abstract: Free analogues of the logarithmic Sobolev inequality compare the relative free Fisher information with the relative free entropy. In the present paper such an inequality is obtained for measures on the circle. The method is based on a random matrix approximation procedure, and a large deviation result concerning the eigenvalue distribution of special unitary matrices is applied and discussed.
TL;DR: In this paper, a Fuchsian group with genus zero and a subgroup of finite index of genus zero was considered and universal recursive formulas for the -series coefficients of any modular form on in terms of those of the canonical Hauptmodul were given.
Abstract: Let be a Fuchsian group of the first kind of genus zero and be a subgroup of of finite index of genus zero. We find universal recursive relations giving the -series coefficients of by using those of the -series of , where is the canonical Hauptmodul for and is a Hauptmodul for without zeros on the complex upper half plane . We find universal recursive formulas for -series coefficients of any modular form on in terms of those of the canonical Hauptmodul .
TL;DR: In this article, it was shown that for d = 2 the equality on the right implies that B is a parallelogram and on the left implies that it is a cross polytope.
Abstract: Given a centrally symmetric convex body B in Ed, we denoteby Md(B) the Minkowski space (i.e., finite dimensional Banach space) with unit ball B. Let K be an arbitrary convex body in M d (B). The relationship between volume V(K) and the Minkowskian thickness (= minimal width) �B(K) of K can naturally be given by the sharp geometric inequality V(K) ≥ �(B) � �B(K) d , where �(B) > 0. As a simple corollary of the Rogers-Shephard inequality we obtain that 2d d � 1 ≤ �(B)/V(B) ≤ 2 d with equality on the left attained if and only if B is the difference body of a simplex and on the right if B is a cross-polytope. The main result of this paper is that for d = 2 the equality on the right implies that B is a parallelogram. The obtained results yield the sharp upper bound for the modified Banach-Mazur distance to the regular hexagon.
TL;DR: In this paper, the authors describe which graphs occur when a finite group of characters is a solvable group of Fitting height 2 and the vertex set is the set of primes dividing the degrees of irreducible characters of the characters.
Abstract: Abstract Given a finite group $G$ , we attach to the character degrees of $G$ a graph whose vertex set is the set of primes dividing the degrees of irreducible characters of $G$ , and with an edge between $p$ and $q$ if $pq$ divides the degree of some irreducible character of $G$ . In this paper, we describe which graphs occur when $G$ is a solvable group of Fitting height 2.
TL;DR: In this article, the authors introduce roots of indecomposable modules over group algebras of finite groups, and investigate some properties of their properties, and correct an error in Landrock's book which has to do with simple modules.
Abstract: Abstract We introduce roots of indecomposable modules over group algebras of finite groups, and we investigate some of their properties. This allows us to correct an error in Landrock's book which has to do with roots of simple modules.
TL;DR: In this article, an upper bound on the first S 1 invariant eigenvalue of the Laplacian for S 2 invariant metrics on S 2 is used to find obstructions to the existence of S 1 equivariant isometric embeddings of such metrics in (R 3, can).
Abstract: A sharp upper bound on the first S 1 invariant eigenvalue of the Laplacian for S 1 invariant metrics on S 2 is used to find obstructions to the existence of S 1 equivariant isometric embeddings of such metrics in (R 3 ,can). As a corollary we prove: If the first four distinct eigenvalues have even multiplicities then the metric cannot be equivariantly, isometrically embedded in (R 3 ,can). This leads to generalizations of some classical results in the theory of surfaces.
TL;DR: In this article, it was shown that the homeomorphism of a Polish space is homeomorphic to a given set of elements in a homeomorphic space, and it was proved that dimT X = inf{dimL X': Xis homeomorphous to X}.
Abstract: Let X be a Polish space. We will prove that dimT X = inf{dimL X ' : Xis homeomorphic to X},
TL;DR: In this paper, the authors describe six pencils of K3-surfaces which have large Picard number (19,20) and each contains precisely five special fibers: four have A-D-E singularities and one is non- reduced.
Abstract: In this paper we describe six pencils of K3-surfaces which have large Picard number (� = 19,20) and each contains precisely five special fibers: four have A-D-E singularities and one is non- reduced. In particular, we characterize these surfaces as cyclic coveringsof some K3-surfaces described in a recent paper by Barth and the author. In many cases, using 3-divisible sets, resp., 2-divisible sets, of rational curves and lattice theory, we describe explicitly the Picard lattices.
TL;DR: For a weakly convergent sequence of integrable unitary connections on a complex vector bundle over a complex manifold, there is a subsequence of local holomorphic frames that converges strongly in an appropriate Holder class as mentioned in this paper.
Abstract: Using a modification ofWebster's proofof theNewlander-Nirenberg theorem, it is shown that, for a weakly convergent sequence of integrable unitary connections on a complex vector bundle over a complex manifold, there is a subsequence of local holomorphic frames that converges strongly in an appropriate Holder class.
TL;DR: In this article, the authors give a geometric proof of classical results that characterize the Pisot numbers as algebraic and identify such numbers as members of Z(� 1) � Z( �)� with nx → 0(mod 1), where Z( ε) is the dual module of ε.
Abstract: We give a geometric proof of classical results that characterize Pisot numbers as algebraic � > 1 for which there is x 6 0 withnx → 0(mod 1) and identify such x as members of Z(� 1) � Z(�)� where Z(�)� is the dual module of Z(�).
TL;DR: In this article, the number of cyclic cubic fields with a given conductor and a given index is determined, where the index is a function of the conductor and the index of the index.
Abstract: Abstract The number of cyclic cubic fields with a given conductor and a given index is determined.
TL;DR: In this article, the authors considered the w�-closed operator algebra A+ generated by the image of the semigroup SL2(R+) under a unitary representation of SL 2(R) on the Hilbert space L 2 (R).
Abstract: We consider the w�-closed operator algebra A+ generated by the image of the semigroup SL2(R+) under a unitary representationof SL2(R) on the Hilbert space L 2 (R). We show that A+ is a reflexive operatoralgebra and A+ = Alg D where D is a double triangle subspace lattice. Surprisingly, A+ is also generated as a w � -closed algebra by the image underof a strict subsemigroup of SL2(R+).