Canadian Journal of Mathematics-Journal Canadien De Mathematiques最新文献_第8页

On ternary Diophantine equations of signature $(p,p,text{3})$ over number fields 数字域上签名$(p,p，text{3})$的三元丢番图方程

IF 0.7 3区数学

Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-06-24 DOI: 10.4153/S0008414X22000311

Erman Isik, Yasemin Kara, Ekin Ozman

引用次数: 1

Classification of generalized Einstein metrics on three-dimensional Lie groups 三维李群上广义爱因斯坦度量的分类

IF 0.7 3区数学

Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-06-02 DOI: 10.4153/S0008414X23000056

V. Cort'es, David Krusche

引用次数: 2

Multilinear transference of Fourier and Schur multipliers acting on noncommutative $L_p$ -spaces 作用于非交换L_p -空间的傅里叶和舒尔乘法器的多线性迁移

IF 0.7 3区数学

Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-06-01 DOI: 10.4153/S0008414X2200058X

M. Caspers, Amudhan Krishnaswamy-Usha, G. Vos

{"title":"Multilinear transference of Fourier and Schur multipliers acting on noncommutative \u0000$L_p$\u0000 -spaces","authors":"M. Caspers, Amudhan Krishnaswamy-Usha, G. Vos","doi":"10.4153/S0008414X2200058X","DOIUrl":"https://doi.org/10.4153/S0008414X2200058X","url":null,"abstract":"Abstract Let G be a locally compact unimodular group, and let \u0000$phi $\u0000 be some function of n variables on G. To such a \u0000$phi $\u0000 , one can associate a multilinear Fourier multiplier, which acts on some n-fold product of the noncommutative \u0000$L_p$\u0000 -spaces of the group von Neumann algebra. One may also define an associated Schur multiplier, which acts on an n-fold product of Schatten classes \u0000$S_p(L_2(G))$\u0000 . We generalize well-known transference results from the linear case to the multilinear case. In particular, we show that the so-called “multiplicatively bounded \u0000$(p_1,ldots ,p_n)$\u0000 -norm” of a multilinear Schur multiplier is bounded above by the corresponding multiplicatively bounded norm of the Fourier multiplier, with equality whenever the group is amenable. Furthermore, we prove that the bilinear Hilbert transform is not bounded as a vector-valued map \u0000$L_{p_1}(mathbb {R}, S_{p_1}) times L_{p_2}(mathbb {R}, S_{p_2}) rightarrow L_{1}(mathbb {R}, S_{1})$\u0000 , whenever \u0000$p_1$\u0000 and \u0000$p_2$\u0000 are such that \u0000$frac {1}{p_1} + frac {1}{p_2} = 1$\u0000 . A similar result holds for certain Calderón–Zygmund-type operators. This is in contrast to the nonvector-valued Euclidean case.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80083888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

CJM volume 74 issue 3 Cover and Back matter CJM第74卷第3期封面和封底

IF 0.7 3区数学

Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-05-30 DOI: 10.4153/s0008414x22000189

引用次数: 0

CJM volume 74 issue 3 Cover and Front matter CJM第74卷第3期封面和封面问题

IF 0.7 3区数学

Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-05-30 DOI: 10.4153/s0008414x22000177

引用次数: 0

Images of multilinear graded polynomials on upper triangular matrix algebras 上三角矩阵代数上的多重线性梯度多项式的象

IF 0.7 3区数学

Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-05-22 DOI: 10.4153/S0008414X22000438

P. Fagundes, P. Koshlukov

引用次数: 8

Club stationary reflection and the special Aronszajn tree property 俱乐部静止反射和特殊的Aronszajn树性质

IF 0.7 3区数学

Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-05-13 DOI: 10.4153/s0008414x22000207

Omer Ben-Neria, Thomas Gilton

{"title":"Club stationary reflection and the special Aronszajn tree property","authors":"Omer Ben-Neria, Thomas Gilton","doi":"10.4153/s0008414x22000207","DOIUrl":"https://doi.org/10.4153/s0008414x22000207","url":null,"abstract":"Abstract We prove that it is consistent that Club Stationary Reflection and the Special Aronszajn Tree Property simultaneously hold on \u0000$omega _2$\u0000 , thereby contributing to the study of the tension between compactness and incompactness in set theory. The poset which produces the final model follows the collapse of an ineffable cardinal first with an iteration of club adding (with anticipation) and second with an iteration specializing Aronszajn trees. In the first part of the paper, we prove a general theorem about specializing Aronszajn trees on \u0000$omega _2$\u0000 after forcing with what we call \u0000$mathcal {F}$\u0000 -Strongly Proper posets, where \u0000$mathcal {F}$\u0000 is either the weakly compact filter or the filter dual to the ineffability ideal. This type of poset, of which the Levy collapse is a degenerate example, uses systems of exact residue functions to create many strongly generic conditions. We prove a new result about stationary set preservation by quotients of this kind of poset; as a corollary, we show that the original Laver–Shelah model, which starts from a weakly compact cardinal, satisfies a strong stationary reflection principle, although it fails to satisfy the full Club Stationary Reflection. In the second part, we show that the composition of collapsing and club adding (with anticipation) is an \u0000$mathcal {F}$\u0000 -Strongly Proper poset. After proving a new result about Aronszajn tree preservation, we show how to obtain the final model.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80890089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Mean square values of L-functions over subgroups for nonprimitive characters, Dedekind sums and bounds on relative class numbers 非基元字符子群上l -函数的均方值、Dedekind和及相对类数的界

IF 0.7 3区数学

Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-05-02 DOI: 10.4153/S0008414X2300010X

S. Louboutin, Marc Munsch

{"title":"Mean square values of L-functions over subgroups for nonprimitive characters, Dedekind sums and bounds on relative class numbers","authors":"S. Louboutin, Marc Munsch","doi":"10.4153/S0008414X2300010X","DOIUrl":"https://doi.org/10.4153/S0008414X2300010X","url":null,"abstract":"Abstract An explicit formula for the mean value of \u0000$vert L(1,chi )vert ^2$\u0000 is known, where \u0000$chi $\u0000 runs over all odd primitive Dirichlet characters of prime conductors p. Bounds on the relative class number of the cyclotomic field \u0000${mathbb Q}(zeta _p)$\u0000 follow. Lately, the authors obtained that the mean value of \u0000$vert L(1,chi )vert ^2$\u0000 is asymptotic to \u0000$pi ^2/6$\u0000 , where \u0000$chi $\u0000 runs over all odd primitive Dirichlet characters of prime conductors \u0000$pequiv 1 pmod {2d}$\u0000 which are trivial on a subgroup H of odd order d of the multiplicative group \u0000$({mathbb Z}/p{mathbb Z})^*$\u0000 , provided that \u0000$dll frac {log p}{log log p}$\u0000 . Bounds on the relative class number of the subfield of degree \u0000$frac {p-1}{2d}$\u0000 of the cyclotomic field \u0000${mathbb Q}(zeta _p)$\u0000 follow. Here, for a given integer \u0000$d_0>1$\u0000 , we consider the same questions for the nonprimitive odd Dirichlet characters \u0000$chi '$\u0000 modulo \u0000$d_0p$\u0000 induced by the odd primitive characters \u0000$chi $\u0000 modulo p. We obtain new estimates for Dedekind sums and deduce that the mean value of \u0000$vert L(1,chi ')vert ^2$\u0000 is asymptotic to \u0000$frac {pi ^2}{6}prod _{qmid d_0}left (1-frac {1}{q^2}right )$\u0000 , where \u0000$chi $\u0000 runs over all odd primitive Dirichlet characters of prime conductors p which are trivial on a subgroup H of odd order \u0000$dll frac {log p}{log log p}$\u0000 . As a consequence, we improve the previous bounds on the relative class number of the subfield of degree \u0000$frac {p-1}{2d}$\u0000 of the cyclotomic field \u0000${mathbb Q}(zeta _p)$\u0000 . Moreover, we give a method to obtain explicit formulas and use Mersenne primes to show that our restriction on d is essentially sharp.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80673771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

On the primality of totally ordered q-factorization graphs 全序q分解图的素数

IF 0.7 3区数学

Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-04-22 DOI: 10.4153/s0008414x23000160

A. Moura, C. Silva

引用次数: 2

Two general series identities involving modified Bessel functions and a class of arithmetical functions 涉及修正贝塞尔函数和一类算术函数的两个一般级数恒等式

IF 0.7 3区数学

Canadian Journal of Mathematics-Journal Canadien De Mathematiques Pub Date : 2022-04-21 DOI: 10.4153/S0008414X22000530

B. Berndt, A. Dixit, Rajat Gupta, A. Zaharescu

{"title":"Two general series identities involving modified Bessel functions and a class of arithmetical functions","authors":"B. Berndt, A. Dixit, Rajat Gupta, A. Zaharescu","doi":"10.4153/S0008414X22000530","DOIUrl":"https://doi.org/10.4153/S0008414X22000530","url":null,"abstract":"Abstract We consider two sequences \u0000$a(n)$\u0000 and \u0000$b(n)$\u0000 , \u0000$1leq n<infty $\u0000 , generated by Dirichlet series \u0000$$ begin{align*}sum_{n=1}^{infty}frac{a(n)}{lambda_n^{s}}qquadtext{and}qquad sum_{n=1}^{infty}frac{b(n)}{mu_n^{s}},end{align*} $$\u0000 satisfying a familiar functional equation involving the gamma function \u0000$Gamma (s)$\u0000 . Two general identities are established. The first involves the modified Bessel function \u0000$K_{mu }(z)$\u0000 , and can be thought of as a ‘modular’ or ‘theta’ relation wherein modified Bessel functions, instead of exponential functions, appear. Appearing in the second identity are \u0000$K_{mu }(z)$\u0000 , the Bessel functions of imaginary argument \u0000$I_{mu }(z)$\u0000 , and ordinary hypergeometric functions \u0000${_2F_1}(a,b;c;z)$\u0000 . Although certain special cases appear in the literature, the general identities are new. The arithmetical functions appearing in the identities include Ramanujan’s arithmetical function \u0000$tau (n)$\u0000 , the number of representations of n as a sum of k squares \u0000$r_k(n)$\u0000 , and primitive Dirichlet characters \u0000$chi (n)$\u0000 .","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2022-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78746052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4