Pub Date : 2019-09-01DOI: 10.1215/21562261-2019-0019
I. Ishikawa
{"title":"Explicit calculation of local integrals for twisted triple product L-functions","authors":"I. Ishikawa","doi":"10.1215/21562261-2019-0019","DOIUrl":"https://doi.org/10.1215/21562261-2019-0019","url":null,"abstract":"","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/21562261-2019-0019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45950118","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}
Pub Date : 2019-09-01DOI: 10.1215/21562261-2019-0018
A. Baklouti, S. Bejar, Ramzi Fendri
{"title":"A local rigidity theorem for finite actions on Lie groups and application to compact extensions of Rn","authors":"A. Baklouti, S. Bejar, Ramzi Fendri","doi":"10.1215/21562261-2019-0018","DOIUrl":"https://doi.org/10.1215/21562261-2019-0018","url":null,"abstract":"","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48379840","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}
Pub Date : 2019-06-02DOI: 10.1215/21562261-2022-0026
O. Nishimura
A formula on Stirling numbers of the second kind $S(n, k)$ is proved. As a corollary, for odd $n$ and even $k$, it is shown that $k!S(n, k)$ is a positive multiple of the greatest common divisor of $j!S(n, j)$ for $k+1leq jleq n$. Also, as an application to algebraic topology, some isomorphisms of unstable $K^1$-groups of stunted complex projective spaces are deduced.
{"title":"A formula on Stirling numbers of the second kind and its application to the unstable K-theory of stunted complex projective spaces","authors":"O. Nishimura","doi":"10.1215/21562261-2022-0026","DOIUrl":"https://doi.org/10.1215/21562261-2022-0026","url":null,"abstract":"A formula on Stirling numbers of the second kind $S(n, k)$ is proved. As a corollary, for odd $n$ and even $k$, it is shown that $k!S(n, k)$ is a positive multiple of the greatest common divisor of $j!S(n, j)$ for $k+1leq jleq n$. Also, as an application to algebraic topology, some isomorphisms of unstable $K^1$-groups of stunted complex projective spaces are deduced.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45370420","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}
Pub Date : 2019-06-01DOI: 10.1215/21562261-2018-0011
V. Valmorin
We build a locally convex algebra of Gevrey type functions defined in the Poincare half-plane in which a class of periodic hyperfunctions on the real line is topologically embedded. This is accomplished via a harmonic regularization method. In this algebra we can give a sense to differential problems involving products of distributions or hyperfunctions which are a priori not defined in the classical setting. Some examples and an application are given.
{"title":"Multiplication of periodic hyperfunctions via harmonic regularization and applications","authors":"V. Valmorin","doi":"10.1215/21562261-2018-0011","DOIUrl":"https://doi.org/10.1215/21562261-2018-0011","url":null,"abstract":"We build a locally convex algebra of Gevrey type functions defined in the Poincare half-plane in which a class of periodic hyperfunctions on the real line is topologically embedded. This is accomplished via a harmonic regularization method. In this algebra we can give a sense to differential problems involving products of distributions or hyperfunctions which are a priori not defined in the classical setting. Some examples and an application are given.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/21562261-2018-0011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44371623","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}
Pub Date : 2019-05-14DOI: 10.1215/21562261-2022-0014
Kotaro Kawatani
Let $mathbf D$ be the homotopy category of a stable infinity category. Then the category $mathbf D^{Delta^1}$ of morphisms in $mathbf{D}$ is also triangulated. Hence the space $mathsf{Stab},{ mathbf D^{Delta^1}}$ of stability conditions on $mathbf D^{Delta^1}$ is well-defined though the non-emptiness of $mathsf{Stab},{ mathbf D^{Delta^1}}$ is not obvious. We discuss a relation between $mathsf{Stab},{ mathbf D^{Delta^1}}$ and $mathsf{Stab},{ mathbf D}$ by proposing some problems.
{"title":"Stability conditions on morphisms in a category","authors":"Kotaro Kawatani","doi":"10.1215/21562261-2022-0014","DOIUrl":"https://doi.org/10.1215/21562261-2022-0014","url":null,"abstract":"Let $mathbf D$ be the homotopy category of a stable infinity category. Then the category $mathbf D^{Delta^1}$ of morphisms in $mathbf{D}$ is also triangulated. Hence the space $mathsf{Stab},{ mathbf D^{Delta^1}}$ of stability conditions on $mathbf D^{Delta^1}$ is well-defined though the non-emptiness of $mathsf{Stab},{ mathbf D^{Delta^1}}$ is not obvious. We discuss a relation between $mathsf{Stab},{ mathbf D^{Delta^1}}$ and $mathsf{Stab},{ mathbf D}$ by proposing some problems.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49179650","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}
Pub Date : 2019-05-02DOI: 10.1215/21562261-2022-0021
Kazushi Kobayashi
By the SYZ construction, a mirror pair $(X,check{X})$ of a complex torus $X$ and a mirror partner $check{X}$ of the complex torus $X$ is described as the special Lagrangian torus fibrations $X rightarrow B$ and $check{X} rightarrow B$ on the same base space $B$. Then, by the SYZ transform, we can construct a simple projectively flat bundle on $X$ from each affine Lagrangian multi section of $check{X} rightarrow B$ with a unitary local system along it. However, there are ambiguities of the choices of transition functions of it, and this causes difficulties when we try to construct a functor between the symplectic geometric category and the complex geometric category. In this paper, we prove that there exists a bijection between the set of the isomorphism classes of their objects by solving this problem.
{"title":"The bijectivity of mirror functors on tori","authors":"Kazushi Kobayashi","doi":"10.1215/21562261-2022-0021","DOIUrl":"https://doi.org/10.1215/21562261-2022-0021","url":null,"abstract":"By the SYZ construction, a mirror pair $(X,check{X})$ of a complex torus $X$ and a mirror partner $check{X}$ of the complex torus $X$ is described as the special Lagrangian torus fibrations $X rightarrow B$ and $check{X} rightarrow B$ on the same base space $B$. Then, by the SYZ transform, we can construct a simple projectively flat bundle on $X$ from each affine Lagrangian multi section of $check{X} rightarrow B$ with a unitary local system along it. However, there are ambiguities of the choices of transition functions of it, and this causes difficulties when we try to construct a functor between the symplectic geometric category and the complex geometric category. In this paper, we prove that there exists a bijection between the set of the isomorphism classes of their objects by solving this problem.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45676436","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}
Pub Date : 2019-04-01DOI: 10.1215/21562261-2018-0005
A. Dubouloz
We show that all complements of cuspidal hyperplane sections of smooth projective cubic surfaces have isomorphic A(2)-cylinders. As a consequence, we derive that the A(2)-cancellation problem fails in every dimension greater than or equal to 2.
{"title":"Affine surfaces with isomorphic A2-cylinders","authors":"A. Dubouloz","doi":"10.1215/21562261-2018-0005","DOIUrl":"https://doi.org/10.1215/21562261-2018-0005","url":null,"abstract":"We show that all complements of cuspidal hyperplane sections of smooth projective cubic surfaces have isomorphic A(2)-cylinders. As a consequence, we derive that the A(2)-cancellation problem fails in every dimension greater than or equal to 2.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2019-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47972918","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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