On a Shimura curve, the reduction modulo a prime $p$ of the Hecke correspondence $T(p)$ yields the congruence relation $PicupPi'$ with $Pi$ being the graph of the Frobenius mapping from the Shimura curve modulo $p$ to itself, and $Pi'$ its transpose. Starting with a curve $C$ of genus $g geq 2$ over $mathbb{F}_p$ together with a subset $mathfrak{S}subset C(mathbb{F}_{p^2})$, Ihara studied the liftability to characteristic $0$ of $PicupPi'$ so that $Pi$ and $Pi'$ are separated outside $mathfrak{S}$ in the lifting. In some case, Ihara obtained the uniqueness of the liftability to characteristic $0$ and gave some necessary and sufficient condition, described by some differential form on $C$, for $(C,mathfrak{S})$ to be liftable to modulo $p^2$. In this paper, in case when $C$ is defined over $mathbb{F}_{p^2}$, we compute complete tables of such $(C,{mathfrak S})$ liftable to modulo $p^2$ for $g=2$ and $3leq p leq 13$ using computer, and as an application of this uniqueness, we identify some particular Shimura curve by its equation.
{"title":"On Congruence Relations and Equations of Shimura Curves","authors":"A. Kurihara","doi":"10.3836/tjm/1502179308","DOIUrl":"https://doi.org/10.3836/tjm/1502179308","url":null,"abstract":"On a Shimura curve, the reduction modulo a prime $p$ of the Hecke correspondence $T(p)$ yields the congruence relation $PicupPi'$ with $Pi$ being the graph of the Frobenius mapping from the Shimura curve modulo $p$ to itself, and $Pi'$ its transpose. Starting with a curve $C$ of genus $g geq 2$ over $mathbb{F}_p$ together with a subset $mathfrak{S}subset C(mathbb{F}_{p^2})$, Ihara studied the liftability to characteristic $0$ of $PicupPi'$ so that $Pi$ and $Pi'$ are separated outside $mathfrak{S}$ in the lifting. In some case, Ihara obtained the uniqueness of the liftability to characteristic $0$ and gave some necessary and sufficient condition, described by some differential form on $C$, for $(C,mathfrak{S})$ to be liftable to modulo $p^2$. In this paper, in case when $C$ is defined over $mathbb{F}_{p^2}$, we compute complete tables of such $(C,{mathfrak S})$ liftable to modulo $p^2$ for $g=2$ and $3leq p leq 13$ using computer, and as an application of this uniqueness, we identify some particular Shimura curve by its equation.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46138579","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}
{"title":"Principal Curvatures of Homogeneous Hypersurfaces in a Grassmann Manifold $widetilde{text{Gr}}_{ 3}(text{Im}mathbb{O})$ by the $G_2$-action","authors":"Kanako Enoyoshi","doi":"10.3836/TJM/1502179291","DOIUrl":"https://doi.org/10.3836/TJM/1502179291","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44867906","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}
{"title":"Compact Commutators of Calderón-Zygmund and Generalized Fractional Integral Operators with a Function in Generalized Campanato Spaces on Generalized Morrey Spaces","authors":"Ryutaro Arai, E. Nakai","doi":"10.3836/TJM/1502179285","DOIUrl":"https://doi.org/10.3836/TJM/1502179285","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48179777","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}
{"title":"Hopf-homoclinic Bifurcations and Heterodimensional Cycles","authors":"Shuntaro Tomizawa","doi":"10.3836/TJM/1502179284","DOIUrl":"https://doi.org/10.3836/TJM/1502179284","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47036580","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}
{"title":"Coincidence Between Two Binary Recurrent Sequences of Polynomials Arising from Diophantine Triples","authors":"T. Miyazaki","doi":"10.3836/TJM/1502179292","DOIUrl":"https://doi.org/10.3836/TJM/1502179292","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48649820","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}
{"title":"A Generating Function to Generalize the Sum Formula for Quadruple Zeta Values","authors":"T. Machide","doi":"10.3836/TJM/1502179282","DOIUrl":"https://doi.org/10.3836/TJM/1502179282","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45926119","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}
{"title":"On Generalised Kummer Congruences and Higher Rank Iwasawa Theory at Arbitrary Weights","authors":"Kwok-Wing Tsoi","doi":"10.3836/TJM/1502179304","DOIUrl":"https://doi.org/10.3836/TJM/1502179304","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42364705","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}
For locally compact Hausdorff spaces $X$ and $Y$, and function algebras $A$ and $B$ on $X$ and $Y$, respectively, surjections $T:A longrightarrow B$ satisfying norm multiplicative condition $|Tf, Tg|_Y =|fg|_X$, $f,gin A$, with respect to the supremum norms, and those satisfying $||Tf|+|Tg||_Y=||f|+|g||_X$ have been extensively studied. Motivated by this, we consider certain (multiplicative or additive) subsemigroups $A$ and $B$ of $C_0(X)$ and $C_0(Y)$, respectively, and study surjections $T: A longrightarrow B$ satisfying the norm condition $rho(Tf, Tg)=rho(f,g)$, $f,g in A$, for some class of two variable positive functions $rho$. It is shown that $T$ is also a composition in modulus map.
{"title":"Composition in Modulus Maps on Semigroups of Continuous\u0000 Functions","authors":"B. Jafarzadeh, F. Sady","doi":"10.3836/TJM/1502179334","DOIUrl":"https://doi.org/10.3836/TJM/1502179334","url":null,"abstract":"For locally compact Hausdorff spaces $X$ and $Y$, and function algebras $A$ and $B$ on $X$ and $Y$, respectively, surjections $T:A longrightarrow B$ satisfying norm multiplicative condition $|Tf, Tg|_Y =|fg|_X$, $f,gin A$, with respect to the supremum norms, and those satisfying $||Tf|+|Tg||_Y=||f|+|g||_X$ have been extensively studied. Motivated by this, we consider certain (multiplicative or additive) subsemigroups $A$ and $B$ of $C_0(X)$ and $C_0(Y)$, respectively, and study surjections $T: A longrightarrow B$ satisfying the norm condition $rho(Tf, Tg)=rho(f,g)$, $f,g in A$, for some class of two variable positive functions $rho$. It is shown that $T$ is also a composition in modulus map.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46930412","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}
We show a method to construct a special Lagrangian submanifold L' from a given special Lagrangian submanifold L in a Calabi-Yau manifold with the use of generalized perpendicular symmetries. We use moment maps of the actions of Lie groups, which are not necessarily abelian. By our method, we construct some non-trivial examples in the cotangent bundles of the spheres which are non-flat Calabi-Yau manifolds equipped with the Stenzel metrics.
{"title":"A Construction of Special Lagrangian Submanifolds by Generalized Perpendicular Symmetries","authors":"Akifumi Ochiai","doi":"10.3836/TJM/1502179306","DOIUrl":"https://doi.org/10.3836/TJM/1502179306","url":null,"abstract":"We show a method to construct a special Lagrangian submanifold L' from a given special Lagrangian submanifold L in a Calabi-Yau manifold with the use of generalized perpendicular symmetries. We use moment maps of the actions of Lie groups, which are not necessarily abelian. By our method, we construct some non-trivial examples in the cotangent bundles of the spheres which are non-flat Calabi-Yau manifolds equipped with the Stenzel metrics.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46316494","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}
{"title":"Hopf Bifurcation and Hopf-Pitchfork Bifurcation in an Integro-Differential Reaction-Diffusion System","authors":"Shunsuke Kobayashi, T. Sakamoto","doi":"10.3836/TJM/1502179295","DOIUrl":"https://doi.org/10.3836/TJM/1502179295","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49570845","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}
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