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Canadian Mathematical Bulletin
Number of Followers: 0  Hybrid journal (It can contain Open Access articles)ISSN (Print) 0008-4395 - ISSN (Online) 1496-4287 Published by Cambridge University Press  [353 journals]
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- BCM volume 68 issue 2 Cover and Front matter
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Pages: 1 - 4
PubDate: 2025-04-23
DOI: 10.4153/S0008439525000426
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- BCM volume 68 issue 2 Cover and Back matter
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Pages: 1 - 2
PubDate: 2025-04-23
DOI: 10.4153/S0008439525000438
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- On the binomial transforms of Apéry-like sequences
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Authors: Liu; Ji-Cai
Pages: 359 - 376
Abstract: In his proof of the irrationality of
and 
, Apéry defined two integer sequences through 
-term recurrences, which are known as the famous Apéry numbers. Zagier, Almkvist–Zudilin, and Cooper successively introduced the other 
sporadic sequences through variants of Apéry’s 
-term recurrences. All of the 
sporadic sequences are called Apéry-like sequences. Motivated by Gessel’s congruences mod 
for the Apéry numbers, we investigate congruences of the form 
for all of the 
Apéry-like sequences 
. Let 
be the largest positive integer such that 
for all non-negative integers n. We determine the values of 
PubDate: 2025-01-08
DOI: 10.4153/S0008439524000924
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- Presentation of an Iwasawa algebra: The pro-p Iwahori of simple, simply
connected, split groups-
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Authors: Lahiri; Aranya, Ray, Jishnu
Pages: 377 - 394
Abstract: In this article, we generalize results of Clozel and Ray (for
and 
, respectively) to give explicit ring-theoretic presentation in terms of a complete set of generators and relations of the Iwasawa algebra of the pro-p Iwahori subgroup of a simple, simply connected, split group 
over 
.
PubDate: 2025-01-09
DOI: 10.4153/S000843952400078X
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- A characterization of the existence of zeros for operators with
Lipschitzian derivative and closed range-
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Authors: Ricceri; Biagio
Pages: 395 - 400
Abstract: Let H be a real Hilbert space and
be a 
operator with Lipschitzian derivative and closed range. We prove that 
if and only if, for each 
, there exist a convex set 
and a convex function 
such that 
and 
.
PubDate: 2025-01-08
DOI: 10.4153/S0008439524000821
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- Generalized torsion orders and Alexander polynomials
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Authors: Ito; Tetsuya
Pages: 401 - 420
Abstract: A nontrivial element of a group is a generalized torsion element if some products of its conjugates is the identity. The minimum number of such conjugates is called a generalized torsion order. We provide several restrictions for generalized torsion orders by using the Alexander polynomial.
PubDate: 2025-01-08
DOI: 10.4153/S0008439524000432
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- Product of two involutions in quaternionic special linear group
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Authors: Gongopadhyay; Krishnendu, Lohan, Tejbir, Maity, Chandan
Pages: 421 - 439
Abstract: An element of a group is called reversible if it is conjugate to its own inverse. Reversible elements are closely related to strongly reversible elements, which can be expressed as a product of two involutions. In this paper, we classify the reversible and strongly reversible elements in the quaternionic special linear group
and quaternionic projective linear group 
. We prove that an element of 
(resp. 
) is reversible if and only if it is a product of two skew-involutions (resp. involutions).
PubDate: 2025-01-08
DOI: 10.4153/S0008439524000699
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- Biderivations of Lie algebras
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Authors: Chen; Qiufan, Yao, Yufeng, Zhao, Kaiming
Pages: 440 - 450
Abstract: In this paper, we first introduce the concept of symmetric biderivation radicals and characteristic subalgebras of Lie algebras and study their properties. Based on these results, we precisely determine biderivations of some Lie algebras including finite-dimensional simple Lie algebras over arbitrary fields of characteristic not
or 
, and the Witt algebras 
over fields of characteristic 
. As an application, commutative post-Lie algebra structure on the aforementioned Lie algebras is shown to be trivial.
PubDate: 2025-01-08
DOI: 10.4153/S0008439524000833
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- Buried points of plane continua
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Authors: Lipham; David, van Mill, Jan, Tuncali, Murat, Tymchatyn, Ed, Valkenburg, Kirsten
Pages: 451 - 460
Abstract: Sets on the boundary of a complementary component of a continuum in the plane have been of interest since the early 1920s. Curry and Mayer defined the buried points of a plane continuum to be the points in the continuum which were not on the boundary of any complementary component. Motivated by their investigations of Julia sets, they asked what happens if the set of buried points of a plane continuum is totally disconnected and nonempty. Curry, Mayer, and Tymchatyn showed that in that case the continuum is Suslinian, i.e., it does not contain an uncountable collection of nondegenerate pairwise disjoint subcontinua. In an answer to a question of Curry et al., van Mill and Tuncali constructed a plane continuum whose buried point set was totally disconnected, nonempty, and one-dimensional at each point of a countably infinite set. In this paper, we show that the van Mill–Tuncali example was the best possible in the sense that whenever the buried set is totally disconnected, it is one-dimensional at each of at most countably many points. As a corollary, we find that the buried set cannot be almost zero-dimensional unless it is zero-dimensional. We also construct locally connected van Mill–Tuncali type examples.
PubDate: 2025-01-08
DOI: 10.4153/S0008439524000894
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- The isotrivial case in the Mordell-Lang conjecture for semiabelian
varieties defined over fields of positive characteristic-
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Authors: Ghioca; Dragos
Pages: 461 - 476
Abstract: Let G be a semiabelian variety defined over a finite subfield of an algebraically closed field K of prime characteristic. We describe the intersection of a subvariety X of G with a finitely generated subgroup of
.
PubDate: 2025-01-13
DOI: 10.4153/S0008439524000468
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- A characterization of virtually free groups among hyperbolic groups
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Authors: Carvalho; André
Pages: 477 - 483
Abstract: We prove that virtually free groups are precisely the hyperbolic groups admitting a language of geodesic words containing a unique representative for each group element with bounded triangles. Equivalently, these are exactly the hyperbolic groups for which the model for the Gromov boundary defined by Silva is well defined.
PubDate: 2025-01-13
DOI: 10.4153/S0008439524000912
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- Spectral identities for Schrödinger operators
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Authors: Guliyev; Namig J.
Pages: 484 - 491
Abstract: We obtain a system of identities relating boundary coefficients and spectral data for the one-dimensional Schrödinger equation with boundary conditions containing rational Herglotz–Nevanlinna functions of the eigenvalue parameter. These identities can be thought of as a kind of mini version of the Gelfand–Levitan integral equation for boundary coefficients only.
PubDate: 2025-01-13
DOI: 10.4153/S0008439524000407
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- Spectral ratios and gaps for Steklov eigenvalues of balls with
revolution-type metrics-
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Authors: Brisson; Jade, Colbois, Bruno, Gittins, Katie
Pages: 492 - 511
Abstract: We investigate upper bounds for the spectral ratios and gaps for the Steklov eigenvalues of balls with revolution-type metrics. We do not impose conditions on the Ricci curvature or on the convexity of the boundary. We obtain optimal upper bounds for the Steklov spectral ratios in dimensions 3 and higher. In dimension 3, we also obtain optimal upper bounds for the Steklov spectral gaps. By imposing additional constraints on the metric, we obtain upper bounds for the Steklov spectral gaps in dimensions 4 and higher.
PubDate: 2025-01-14
DOI: 10.4153/S0008439524000778
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- Products of commutators in matrix rings
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Authors: Brešar; Matej, Gardella, Eusebio, Thiel, Hannes
Pages: 512 - 529
Abstract: Let R be a ring and let
. We discuss the question of whether every element in the matrix ring 
is a product of (additive) commutators 
, for 
. An example showing that this does not always hold, even when R is commutative, is provided. If, however, R has Bass stable rank one, then under various additional conditions every element in 
is a product of three commutators. Further, if R is a division ring with infinite center, then every element in 
is a product of two commutators. If R is a field and 
, then every element in 
is a sum of elements of the form 
with 
if and only if the degree of the minimal polynomial of a is greater than 
.
PubDate: 2025-01-14
DOI: 10.4153/S0008439524000523
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- Control theorems for Hilbert modular varieties
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Authors: Sheth; Arshay
Pages: 530 - 549
Abstract: We prove an exact control theorem, in the sense of Hida theory, for the ordinary part of the middle degree étale cohomology of certain Hilbert modular varieties, after localizing at a suitable maximal ideal of the Hecke algebra. Our method of proof builds upon the techniques introduced by Loeffler–Rockwood–Zerbes (2023, Spherical varieties and p-adic families of cohomology classes); another important ingredient in our proof is the recent work of Caraiani–Tamiozzo (2023, Compositio Mathematica 159, 2279–2325) on the vanishing of the étale cohomology of Hilbert modular varieties with torsion coefficients outside the middle degree. This work will be used in forthcoming work of the author to show that the Asai–Flach Euler system corresponding to a quadratic Hilbert modular form varies in Hida families.
PubDate: 2025-01-14
DOI: 10.4153/S0008439524000791
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- Realizations of free actions via their fixed point algebras
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Authors: Schwieger; Kay, Wagner, Stefan
Pages: 568 - 581
Abstract: Let G be a compact group, let
be a unital C
-algebra, and let 
be a free C
-dynamical system, in the sense of Ellwood, with fixed point algebra 
. We prove that 
can be realized as the G-continuous part of the invariants of an equivariant coaction of G on a corner of 
for a certain Hilbert space 
that arises from the freeness of the action. This extends a result by Wassermann for free and ergodic C
-dynamical systems. As an application, we show that any faithful 
-representation of 
on a Hilbert space 
gives rise to a faithful covariant representation of 
PubDate: 2025-01-17
DOI: 10.4153/S0008439524000808
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- A characterization of inner product spaces via norming vectors
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Authors: Aubrun; Guillaume, Cavichioli, Mathis
Pages: 598 - 602
Abstract: A finite-dimensional normed space is an inner product space if and only if the set of norming vectors of any endomorphism is a linear subspace. This theorem was proved by Sain and Paul for real scalars. In this paper, we give a different proof which also extends to the case of complex scalars.
PubDate: 2025-01-03
DOI: 10.4153/S0008439524000985
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- Small Mahler measures with bounds on the house and shortness
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Authors: El-Serafy; Salma, McKee, James
Pages: 603 - 619
Abstract: We show that for any
, the number of monic, reciprocal, length-
integer polynomials that have house at least 
is finite. The proof is algorithmic, and we are consequently able to compute a complete list (not imposing any bound on the degree) of small Mahler measures of length-
polynomials that have house at least 
.For larger lengths, the analogous finiteness statement is false, as we show by examples. For length 
we show that if one also imposes an upper bound for the Mahler measure that is strictly below the smallest Pisot number 
, and if the length 
polynomial is a cyclotomic multiple of an irreducible polynomial, then the number of polynomials with house at least 
is finite.We pursue these ideas to search opportunistically for small Mahler measures represented by longer polynomials. We find one new small measure.We give an algorithm that finds all Salem numbers in an interval 
that are the Mahler measure of an integer polynomial of length at most 
, provided 
.
PubDate: 2025-01-20
DOI: 10.4153/S0008439524000900
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