In this paper, we construct a right-angled 5-polytope P of finite volume such that all the right-angled Coxeter groups with Fuchsian ends obtained from P are locally rigid.
{"title":"Locally Rigid Right-angled Coxeter Groups with Fuchsian Ends in Dimension 5","authors":"Tomoshige Yukita","doi":"10.3836/tjm/1502179360","DOIUrl":"https://doi.org/10.3836/tjm/1502179360","url":null,"abstract":"In this paper, we construct a right-angled 5-polytope P of finite volume such that all the right-angled Coxeter groups with Fuchsian ends obtained from P are locally rigid.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45929492","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 any transitive piecewise monotonic map for which the set of periodic measures is dense in the set of ergodic invariant measures (such as linear mod $1$ transformations and generalized $beta$-transformations), we show that the set of points for which the Birkhoff average of a continuous function does not exist (called the irregular set) is either empty or has full topological entropy. This generalizes Thompson's theorem for irregular sets of $beta$-transformations, and reduces a complete description of irregular sets of transitive piecewise monotonic maps to Hofbauer-Raith problem on the density of periodic measures.
{"title":"Irregular Sets for Piecewise Monotonic Maps","authors":"Yushi Nakano, Kenichiro Yamamoto","doi":"10.3836/tjm/1502179349","DOIUrl":"https://doi.org/10.3836/tjm/1502179349","url":null,"abstract":"For any transitive piecewise monotonic map for which the set of periodic measures is dense in the set of ergodic invariant measures (such as linear mod $1$ transformations and generalized $beta$-transformations), we show that the set of points for which the Birkhoff average of a continuous function does not exist (called the irregular set) is either empty or has full topological entropy. This generalizes Thompson's theorem for irregular sets of $beta$-transformations, and reduces a complete description of irregular sets of transitive piecewise monotonic maps to Hofbauer-Raith problem on the density of periodic measures.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41347528","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":"Quiver Representations, Group Characters, and Prime Graphs of Finite Groups","authors":"N. Iiyori, M. Sawabe","doi":"10.3836/TJM/1502179297","DOIUrl":"https://doi.org/10.3836/TJM/1502179297","url":null,"abstract":"","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":"42 1","pages":"497-523"},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41681375","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}
In this paper, we introduce the higher order hypergeometric Euler numbers and show several interesting expressions. In 1875, Glaisher gave several interesting determinant expressions of numbers, including Bernoulli, Cauchy and Euler numbers. One advantage of hypergeometric numbers, including Bernoulli, Cauchy and Euler hypergeometric numbers, is the natural extension of determinant expressions of the numbers. As applications, we can get the inversion relations such that Euler numbers are elements in the determinant.
{"title":"Several Properties of Multiple Hypergeometric Euler Numbers","authors":"T. Komatsu, Wenpeng Zhang","doi":"10.3836/TJM/1502179290","DOIUrl":"https://doi.org/10.3836/TJM/1502179290","url":null,"abstract":"In this paper, we introduce the higher order hypergeometric Euler numbers and show several interesting expressions. In 1875, Glaisher gave several interesting determinant expressions of numbers, including Bernoulli, Cauchy and Euler numbers. One advantage of hypergeometric numbers, including Bernoulli, Cauchy and Euler hypergeometric numbers, is the natural extension of determinant expressions of the numbers. As applications, we can get the inversion relations such that Euler numbers are elements in the determinant.","PeriodicalId":48976,"journal":{"name":"Tokyo Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42382968","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}
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":"42 1","pages":"525-550"},"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":"42 1","pages":"571-584"},"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":"42 1","pages":"471-496"},"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":"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":"42 1","pages":"611-619"},"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":"42 1","pages":"329-355"},"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}
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