{"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}
{"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}