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Tokyo Journal of Mathematics最新文献

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On the $lambda$-invariant of Selmer Groups Arising from Certain Quadratic Twists of Gross Curves 由某些粗糙曲线的二次扭转引起的Selmer群的$ λ $-不变量
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2021-07-07 DOI: 10.3836/tjm/1502179379
Jianing Li
{"title":"On the $lambda$-invariant of Selmer Groups Arising from Certain Quadratic Twists of Gross Curves","authors":"Jianing Li","doi":"10.3836/tjm/1502179379","DOIUrl":"https://doi.org/10.3836/tjm/1502179379","url":null,"abstract":"Let q be a prime with q ≡ 7 mod 8, and let K = Q( √ −q). Then 2 splits in K, and we write p for either of the primes K above 2. Let K∞ be the unique Z2-extension of K unramified outside p with n-th layer Kn. For certain quadratic and biquadratic extensions F/K, we prove a simple exact formula for the λ-invariant of the Galois group of the maximal abelian 2-extension unramified outside p of the field F∞ = FK∞. Equivalently, our result determines the exact Z2-corank of certain Selmer groups over F∞ of a large family of quadratic twists of the higher dimensional abelian variety with complex multiplication, which is the restriction of scalars to K of the Gross curve with complex multiplication defined over the Hilbert class field of K. We also discuss computations of the associated Selmer groups over Kn in the case when the λ-invariant is equal to 1.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44368783","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: 1
A New Family of Latitudinally Corrugated Two-spheres of Revolution with Simple Cut Locus Structure 具有简单切割轨迹结构的一种新的纬向波纹双转球族
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2021-06-08 DOI: 10.3836/tjm/1502179366
Minoru Tanaka, T. Akamatsu, R. Sinclair, M. Yamaguchi
{"title":"A New Family of Latitudinally Corrugated Two-spheres of Revolution with Simple Cut Locus Structure","authors":"Minoru Tanaka, T. Akamatsu, R. Sinclair, M. Yamaguchi","doi":"10.3836/tjm/1502179366","DOIUrl":"https://doi.org/10.3836/tjm/1502179366","url":null,"abstract":"There are not so many kinds of surface of revolution whose cut locus structure have been determined, although the cut locus structures of very familiar surfaces of revolution (in Euclidean space) such as ellipsoids, 2-sheeted hyperboloids, paraboloids and tori are now known. Except for tori, the known cut locus structures are very simple, i.e., a single point or an arc. In this article, a new family {Mn}n of 2-spheres of revolution with simple cut locus structure is introduced. This family is also new in the sense that the number of points on each meridian which assume a local minimum or maximum of the Gaussian curvature function on the meridian goes to infinity as n tends to infinity. Thus, our family includes surfaces which have arbitrarily many bands of alternately increasing or decreasing Gaussian curvature, although each member of this family has a simple cut locus structure.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41307926","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
On Syntomic Complexes with Modulus for Semi-stable Reduction Cases 半稳定还原情形下的模合原子配合物
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2021-06-01 DOI: 10.3836/tjm/1502179342
Kento Yamamoto
{"title":"On Syntomic Complexes with Modulus for Semi-stable Reduction Cases","authors":"Kento Yamamoto","doi":"10.3836/tjm/1502179342","DOIUrl":"https://doi.org/10.3836/tjm/1502179342","url":null,"abstract":"In this paper, we define a syntomic complex for modulus pair $(X,D)$, where $X$ is a regular semi-stable family and $D$ is an effective Cartier divisor on $X$ and we compute its cohomology sheaves. We construct a symbol map for this syntomic complex for modulus pair $(X,D)$ and investigate its cokernel by computing its cohomology sheaves. To compute the structure of the cohomology sheaves of syntomic complex with modulus, we define some filtrations on it.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43028180","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
Computation of Some Leafwise Cohomology Ring 某些叶上同调环的计算
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2021-03-11 DOI: 10.3836/tjm/1502179396
S. Mori
{"title":"Computation of Some Leafwise Cohomology Ring","authors":"S. Mori","doi":"10.3836/tjm/1502179396","DOIUrl":"https://doi.org/10.3836/tjm/1502179396","url":null,"abstract":"Let $G$ be the group $SL(2,mathbb{R})$, $Psubset G$ be the parabolic subgroup of upper triangular matrices and $Gammasubset G$ be a cocompact lattice. A right action of $P$ on $Gammabackslash G$ defines an orbit foliation $mathcal{F}_P$. We compute the leafwise cohomology ring $H^*(mathcal{F}_P)$ by exploiting non-abelian harmonic analysis on $G$.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48424965","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
A Multi-parameter Family of Self-avoiding Walks on the Sierpiński Gasket Sierpiński垫片上的多参数自回避行走族
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2021-03-01 DOI: 10.3836/TJM/1502179338
T. Otsuka
{"title":"A Multi-parameter Family of Self-avoiding Walks on the\u0000 Sierpiński Gasket","authors":"T. Otsuka","doi":"10.3836/TJM/1502179338","DOIUrl":"https://doi.org/10.3836/TJM/1502179338","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48323683","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
Geometric Properties of Orbits of Hermann actions 赫尔曼作用轨道的几何性质
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2021-01-04 DOI: 10.3836/tjm/1502179367
S. Ohno
{"title":"Geometric Properties of Orbits of Hermann actions","authors":"S. Ohno","doi":"10.3836/tjm/1502179367","DOIUrl":"https://doi.org/10.3836/tjm/1502179367","url":null,"abstract":"In this paper, we investigate properties of orbits of Hermann actions as submanifolds without assuming the commutability of involutions which define Hermann actions. In particular, we compute the second fundamental form of orbits of Hermann action, and give a sufficient condition for orbits of Hermann action to be weakly reflective (resp. arid) submanifolds.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43824839","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: 1
Construction of Solutions of the Classical Field Equation of a Massless Klein-Gordon Field Interacting with a Static Source 与静态源相互作用的无质量Klein-Gordon场经典场方程解的构造
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.3836/TJM/1502179328
Toshimitsu Takaesu
{"title":"Construction of Solutions of the Classical Field Equation of a Massless Klein-Gordon Field Interacting with a Static Source","authors":"Toshimitsu Takaesu","doi":"10.3836/TJM/1502179328","DOIUrl":"https://doi.org/10.3836/TJM/1502179328","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70165763","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
Reverses of Operator Féjer's Inequalities 算子fsamjer不等式的反转
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.3836/TJM/1502179330
S. Dragomir
{"title":"Reverses of Operator Féjer's Inequalities","authors":"S. Dragomir","doi":"10.3836/TJM/1502179330","DOIUrl":"https://doi.org/10.3836/TJM/1502179330","url":null,"abstract":"Let $f$ be an operator convex function on $I$ and $A,$ $Bin mathcal{SA}_{I}left( Hright) ,$ the convex set of selfadjoint operators with spectra in $I.$ If $Aneq B$ and $f,$ as an operator function, is G^{a}teaux differentiable on begin{equation*} [ A,B] :=left{ ( 1-t) A+tB mid tin [ 0,1] right} ,, end{equation*} while $p:[ 0,1] rightarrow lbrack 0,infty )$ is Lebesgue integrable and symmetric, namely $pleft( 1-tright) $ $=pleft( tright) $ for all $tin [ 0,1] ,$ then begin{align*} 0& leq int_{0}^{1}pleft( tright) fleft( left( 1-tright) A+tBright) dt-left( int_{0}^{1}pleft( tright) dtright) fleft( frac{A+B}{2}right) & leq frac{1}{2}left( int_{0}^{1}leftvert t-frac{1}{2}rightvert pleft( tright) dtright) left[ nabla f_{B}left( B-Aright) -nabla f_{A}left( B-Aright) right] end{align*} and begin{align*} 0& leq left( int_{0}^{1}pleft( tright) dtright) frac{fleft( Aright) +fleft( Bright) }{2}-int_{0}^{1}pleft( tright) fleft( left( 1-tright) A+tBright) dt & leq frac{1}{2}int_{0}^{1}left( frac{1}{2}-leftvert t-frac{1}{2} rightvert right) pleft( tright) dtleft[ nabla f_{B}left( B-Aright) -nabla f_{A}left( B-Aright) right] ,. end{align*} Two particular examples of interest are also given.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70165783","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: 8
On the Class Group of an Imaginary Cyclic Field of Conductor $8p$ and $2$-power Degree 导体$8p$和$2$幂次虚循环场的类群
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2021-01-01 DOI: 10.3836/TJM/1502179326
H. Ichimura, Hiroki Sumida-Takahashi
{"title":"On the Class Group of an Imaginary Cyclic Field of Conductor $8p$ and $2$-power Degree","authors":"H. Ichimura, Hiroki Sumida-Takahashi","doi":"10.3836/TJM/1502179326","DOIUrl":"https://doi.org/10.3836/TJM/1502179326","url":null,"abstract":"Let $p=2^{e+1}q+1$ be an odd prime number with $2 nmid q$. Let $K$ be the imaginary cyclic field of conductor $p$ and degree $2^{e+1}$. We denote by $mathcal{F}$ the imaginary quadratic subextension of the imaginary $(2,,2)$-extension $K(sqrt{2})/K^+$ with $mathcal{F} neq K$. We determine the Galois module structure of the $2$-part of the class group of $mathcal{F}$.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70165720","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
Contracted Ideals of $p$-adic Integral Group Rings $p$adic积分群环的压缩理想
IF 0.6 4区 数学
Tokyo Journal of Mathematics Pub Date : 2020-12-01 DOI: 10.3836/tjm/1502179313
Joongul Lee
{"title":"Contracted Ideals of $p$-adic Integral Group Rings","authors":"Joongul Lee","doi":"10.3836/tjm/1502179313","DOIUrl":"https://doi.org/10.3836/tjm/1502179313","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48266253","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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