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Arithmetically equivalent fields in a Galois extension with Frobenius Galois group of 2-power degree 具有2-幂次Frobenius-Galois群的Galois推广中的算术等价域
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-06-13 DOI: 10.4153/S0008439522000388
Masanari Kida
{"title":"Arithmetically equivalent fields in a Galois extension with Frobenius Galois group of 2-power degree","authors":"Masanari Kida","doi":"10.4153/S0008439522000388","DOIUrl":"https://doi.org/10.4153/S0008439522000388","url":null,"abstract":"Abstract Let \u0000$F_{2^n}$\u0000 be the Frobenius group of degree \u0000$2^n$\u0000 and of order \u0000$2^n ( 2^n-1)$\u0000 with \u0000$n ge 4$\u0000 . We show that if \u0000$K/mathbb {Q} $\u0000 is a Galois extension whose Galois group is isomorphic to \u0000$F_{2^n}$\u0000 , then there are \u0000$dfrac {2^{n-1} +(-1)^n }{3}$\u0000 intermediate fields of \u0000$K/mathbb {Q} $\u0000 of degree \u0000$4 (2^n-1)$\u0000 such that they are not conjugate over \u0000$mathbb {Q}$\u0000 but arithmetically equivalent over \u0000$mathbb {Q}$\u0000 . We also give an explicit method to construct these arithmetically equivalent fields.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44014000","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0
Magnitude and Holmes–Thompson intrinsic volumes of convex bodies 凸体的大小和Holmes-Thompson内禀体积
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-06-06 DOI: 10.4153/S0008439522000728
M. Meckes
{"title":"Magnitude and Holmes–Thompson intrinsic volumes of convex bodies","authors":"M. Meckes","doi":"10.4153/S0008439522000728","DOIUrl":"https://doi.org/10.4153/S0008439522000728","url":null,"abstract":"Abstract Magnitude is a numerical invariant of compact metric spaces, originally inspired by category theory and now known to be related to myriad other geometric quantities. Generalizing earlier results in \u0000$ell _1^n$\u0000 and Euclidean space, we prove an upper bound for the magnitude of a convex body in a hypermetric normed space in terms of its Holmes–Thompson intrinsic volumes. As applications of this bound, we give short new proofs of Mahler’s conjecture in the case of a zonoid and Sudakov’s minoration inequality.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44958529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Quasisymmetric harmonics of the exterior algebra 外代数的拟对称调和
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-06-04 DOI: 10.4153/S0008439523000024
N. Bergeron, K. Chan, F. Soltani, M. Zabrocki
{"title":"Quasisymmetric harmonics of the exterior algebra","authors":"N. Bergeron, K. Chan, F. Soltani, M. Zabrocki","doi":"10.4153/S0008439523000024","DOIUrl":"https://doi.org/10.4153/S0008439523000024","url":null,"abstract":"Abstract We study the ring of quasisymmetric polynomials in n anticommuting (fermionic) variables. Let \u0000$R_n$\u0000 denote the ring of polynomials in n anticommuting variables. The main results of this paper show the following interesting facts about quasisymmetric polynomials in anticommuting variables: (1) The quasisymmetric polynomials in \u0000$R_n$\u0000 form a commutative subalgebra of \u0000$R_n$\u0000 . (2) There is a basis of the quotient of \u0000$R_n$\u0000 by the ideal \u0000$I_n$\u0000 generated by the quasisymmetric polynomials in \u0000$R_n$\u0000 that is indexed by ballot sequences. The Hilbert series of the quotient is given by \u0000$$ begin{align*}text{Hilb}_{R_n/I_n}(q) = sum_{k=0}^{lfloor{n/2}rfloor} f^{(n-k,k)} q^k,,end{align*} $$\u0000 where \u0000$f^{(n-k,k)}$\u0000 is the number of standard tableaux of shape \u0000$(n-k,k)$\u0000 . (3) There is a basis of the ideal generated by quasisymmetric polynomials that is indexed by sequences that break the ballot condition.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44232527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0
The error term in the truncated Perron formula for the logarithm of an -function 函数对数的截断的Perron公式中的误差项
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-06-03 DOI: 10.4153/s0008439523000218
S. Garcia, J. Lagarias, Ethan S. Lee
{"title":"The error term in the truncated Perron formula for the logarithm of an -function","authors":"S. Garcia, J. Lagarias, Ethan S. Lee","doi":"10.4153/s0008439523000218","DOIUrl":"https://doi.org/10.4153/s0008439523000218","url":null,"abstract":"We improve upon the traditional error term in the truncated Perron formula for the logarithm of an $L$-function. All our constants are explicit.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45387011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0
BCM volume 65 issue 2 Cover and Front matter BCM第65卷第2期封面和封面
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-05-25 DOI: 10.4153/s0008439522000303
June juin, J. Mashreghi, K. Bringmann, Alessandro Gambini, Remis Tonon
{"title":"BCM volume 65 issue 2 Cover and Front matter","authors":"June juin, J. Mashreghi, K. Bringmann, Alessandro Gambini, Remis Tonon","doi":"10.4153/s0008439522000303","DOIUrl":"https://doi.org/10.4153/s0008439522000303","url":null,"abstract":"","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45469943","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0
BCM volume 65 issue 2 Cover and Back matter BCM第65卷第2期封面和封底
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-05-25 DOI: 10.4153/s0008439522000315
{"title":"BCM volume 65 issue 2 Cover and Back matter","authors":"","doi":"10.4153/s0008439522000315","DOIUrl":"https://doi.org/10.4153/s0008439522000315","url":null,"abstract":"","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46878938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0
CONCORDANCE OF SPATIAL GRAPHS 空间图的一致性
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-05-23 DOI: 10.4153/S000843952300019X
Egor Lappo
{"title":"CONCORDANCE OF SPATIAL GRAPHS","authors":"Egor Lappo","doi":"10.4153/S000843952300019X","DOIUrl":"https://doi.org/10.4153/S000843952300019X","url":null,"abstract":"We define smooth notions of concordance and sliceness for spatial graphs. We prove that sliceness of a spatial graph is equivalent to a condition on a set of linking numbers together with sliceness of a link associated to the graph. This generalizes the result of Taniyama for $theta$-curves.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48785384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0
Zeros in the character tables of symmetric groups with an $ell $ -core index 具有$ell$核心索引的对称群的字符表中的零
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-05-19 DOI: 10.4153/S0008439522000443
Eleanor Mcspirit, K. Ono
{"title":"Zeros in the character tables of symmetric groups with an \u0000$ell $\u0000 -core index","authors":"Eleanor Mcspirit, K. Ono","doi":"10.4153/S0008439522000443","DOIUrl":"https://doi.org/10.4153/S0008439522000443","url":null,"abstract":"Abstract Let \u0000$mathcal {C}_n =left [chi _{lambda }(mu )right ]_{lambda , mu }$\u0000 be the character table for \u0000$S_n,$\u0000 where the indices \u0000$lambda $\u0000 and \u0000$mu $\u0000 run over the \u0000$p(n)$\u0000 many integer partitions of \u0000$n.$\u0000 In this note, we study \u0000$Z_{ell }(n),$\u0000 the number of zero entries \u0000$chi _{lambda }(mu )$\u0000 in \u0000$mathcal {C}_n,$\u0000 where \u0000$lambda $\u0000 is an \u0000$ell $\u0000 -core partition of \u0000$n.$\u0000 For every prime \u0000$ell geq 5,$\u0000 we prove an asymptotic formula of the form \u0000$$ begin{align*}Z_{ell}(n)sim alpha_{ell}cdot sigma_{ell}(n+delta_{ell})p(n)gg_{ell} n^{frac{ell-5}{2}}e^{pisqrt{2n/3}}, end{align*} $$\u0000 where \u0000$sigma _{ell }(n)$\u0000 is a twisted Legendre symbol divisor function, \u0000$delta _{ell }:=(ell ^2-1)/24,$\u0000 and \u0000$1/alpha _{ell }>0$\u0000 is a normalization of the Dirichlet L-value \u0000$Lleft (left ( frac {cdot }{ell } right ),frac {ell -1}{2}right ).$\u0000 For primes \u0000$ell $\u0000 and \u0000$n>ell ^6/24,$\u0000 we show that \u0000$chi _{lambda }(mu )=0$\u0000 whenever \u0000$lambda $\u0000 and \u0000$mu $\u0000 are both \u0000$ell $\u0000 -cores. Furthermore, if \u0000$Z^*_{ell }(n)$\u0000 is the number of zero entries indexed by two \u0000$ell $\u0000 -cores, then, for \u0000$ell geq 5$\u0000 , we obtain the asymptotic \u0000$$ begin{align*}Z^*_{ell}(n)sim alpha_{ell}^2 cdot sigma_{ell}( n+delta_{ell})^2 gg_{ell} n^{ell-3}. end{align*} $$","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48127336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 3
Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action 具有Taft代数作用的二阶上三角矩阵代数的Specht性质
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-05-16 DOI: 10.4153/S0008439522000327
L. Centrone, Alejandro Estrada
{"title":"Specht property for the algebra of upper triangular matrices of size two with a Taft’s algebra action","authors":"L. Centrone, Alejandro Estrada","doi":"10.4153/S0008439522000327","DOIUrl":"https://doi.org/10.4153/S0008439522000327","url":null,"abstract":"Abstract Let F be a field of characteristic zero, and let \u0000$UT_2$\u0000 be the algebra of \u0000$2 times 2$\u0000 upper triangular matrices over F. In a previous paper by Centrone and Yasumura, the authors give a description of the action of Taft’s algebras \u0000$H_m$\u0000 on \u0000$UT_2$\u0000 and its \u0000$H_m$\u0000 -identities. In this paper, we give a complete description of the space of multilinear \u0000$H_m$\u0000 -identities in the language of Young diagrams through the representation theory of the hyperoctahedral group. We finally prove that the variety of \u0000$H_m$\u0000 -module algebras generated by \u0000$UT_2$\u0000 has the Specht property, i.e., every \u0000$T^{H_m}$\u0000 -ideal containing the \u0000$H_m$\u0000 -identities of \u0000$UT_2$\u0000 is finitely based.","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47873905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0
Analytic Besov spaces, approximation, and closed ideals 解析贝索夫空间，近似和封闭理想
IF 0.6 4区 数学
Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques Pub Date : 2022-05-13 DOI: 10.4153/S0008439522000285
Hafid Bahajji-El Idrissi, Hamza El Azhar
{"title":"Analytic Besov spaces, approximation, and closed ideals","authors":"Hafid Bahajji-El Idrissi, Hamza El Azhar","doi":"10.4153/S0008439522000285","DOIUrl":"https://doi.org/10.4153/S0008439522000285","url":null,"abstract":"Abstract In this paper, we give a complete description of closed ideals of the Banach algebra \u0000$mathcal {B}^{s}_{p}cap lambda _{alpha }$\u0000 , where \u0000$mathcal {B}^{s}_{p}$\u0000 denotes the analytic Besov space and \u0000$lambda _{alpha }$\u0000 is the separable analytic Lipschitz space. Our result extends several previous results in Bahajji-El Idrissi and El-Fallah (2020, Studia Mathematica 255, 209–217), Bouya (2009, Canadian Journal of Mathematics 61, 282–298), and Shirokov (1982, Izv. Ross. Akad. Nauk Ser. Mat. 46, 1316–1332).","PeriodicalId":55280,"journal":{"name":"Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49055172","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 0
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