: In this article, we prove the meromorphic continuation of the multiple Fibonacci zeta functions of depth 2: where F n is the n -th Fibonacci number, Re ð s 1 Þ > 0 and Re ð s 2 Þ > 0 . We compute a complete list of its poles and their residues. We also prove that multiple Fibonacci zeta values at negative integer arguments are rational.
在本文中，我们证明了深度为2的多个Fibonacci zeta函数的亚纯延拓，其中fn是第n个Fibonacci数，Re ð s 1 Þ > 0, Re ð s 2 Þ > 0。我们计算了它的极点及其残数的完整列表。我们也证明了多个Fibonacci zeta值在负整数参数上是有理数。
{"title":"Analytic continuation of the multiple Fibonacci zeta functions","authors":"S. S. Rout, N. K. Meher","doi":"10.3792/PJAA.94.64","DOIUrl":"https://doi.org/10.3792/PJAA.94.64","url":null,"abstract":": In this article, we prove the meromorphic continuation of the multiple Fibonacci zeta functions of depth 2: where F n is the n -th Fibonacci number, Re ð s 1 Þ > 0 and Re ð s 2 Þ > 0 . We compute a complete list of its poles and their residues. We also prove that multiple Fibonacci zeta values at negative integer arguments are rational.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76090629","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}
This note is a summary of our work [OO] which provides an explicit and global moduli-theoretic framework for the collapsing of Ricci-flat Kahler metrics and we use it to study especially the K3 surfaces case. For instance, it allows us to discuss their Gromov-Hausdorff limits along any sequences, which are even not necessarily "maximally degenerating". Our results also give a proof of Kontsevich-Soibelman [KS04, Conjecture 1] (cf., [GW00, Conjecture 6.2]) in the case of K3 surfaces as a byproduct.
{"title":"Collapsing K3 surfaces and Moduli compactification","authors":"Y. Odaka, Y. Oshima","doi":"10.3792/pjaa.94.81","DOIUrl":"https://doi.org/10.3792/pjaa.94.81","url":null,"abstract":"This note is a summary of our work [OO] which provides an explicit and global moduli-theoretic framework for the collapsing of Ricci-flat Kahler metrics and we use it to study especially the K3 surfaces case. For instance, it allows us to discuss their Gromov-Hausdorff limits along any sequences, which are even not necessarily \"maximally degenerating\". Our results also give a proof of Kontsevich-Soibelman [KS04, Conjecture 1] (cf., [GW00, Conjecture 6.2]) in the case of K3 surfaces as a byproduct.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82981400","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 study a relation between the cohomology ring of a regular nilpotent Hessenberg variety and Schubert polynomials. To describe an explicit presentation of the cohomology ring of a regular nilpotent Hessenberg variety, polynomials $f_{i,j}$ were introduced by Abe-Harada-Horiguchi-Masuda. We show that every polynomial $f_{i,j}$ is an alternating sum of certain Schubert polynomials.
{"title":"The cohomology rings of regular nilpotent Hessenberg varieties and Schubert polynomials","authors":"T. Horiguchi","doi":"10.3792/PJAA.94.87","DOIUrl":"https://doi.org/10.3792/PJAA.94.87","url":null,"abstract":"In this paper we study a relation between the cohomology ring of a regular nilpotent Hessenberg variety and Schubert polynomials. To describe an explicit presentation of the cohomology ring of a regular nilpotent Hessenberg variety, polynomials $f_{i,j}$ were introduced by Abe-Harada-Horiguchi-Masuda. We show that every polynomial $f_{i,j}$ is an alternating sum of certain Schubert polynomials.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78731831","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}
The normalization of an irreducible quasi-log canonical pair naturally becomes a quasi-log canonical pair.
不可约的拟对数正则对的归一化自然成为拟对数正则对。
{"title":"On normalization of quasi-log canonical pairs","authors":"O. Fujino, Haidong Liu","doi":"10.3792/pjaa.94.97","DOIUrl":"https://doi.org/10.3792/pjaa.94.97","url":null,"abstract":"The normalization of an irreducible quasi-log canonical pair naturally becomes a quasi-log canonical pair.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2017-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85958233","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}
Stembridge characterizes regular crystals associated with a simply-laced GCM in terms of local graph-theoretic quantities. We give a similar axiomatization for $B_2$ regular crystals (and thus for regular crystals of finite GCM except $G_2$ and affine GCM except $A^{(1)}_{1},G^{(1)}_{2},A^{(2)}_{2},D^{(3)}_4$). Our motivation comes from a generalization of Schur partition theorem by the author jointly with Masaki Watanabe proved indirectly via theory of perfect crystal.
Stembridge用局部图论量描述了与简单带状GCM相关的规则晶体。对于$B_2$规则晶体，我们给出了类似的公理化(因此对于除$G_2$外的有限GCM的规则晶体和除$ a ^{(1)}_{1}，G^{(1)}_{2}， a ^{(2)}_{2}，D^{(3)}_4$外的仿射GCM)。我们的动机来自于作者与渡边雅明共同对Schur分拆定理的推广，并通过完美晶体理论间接证明。
{"title":"A local characterization of $B_{2}$ regular crystals","authors":"Shunsuke Tsuchioka","doi":"10.3792/pjaa.97.010","DOIUrl":"https://doi.org/10.3792/pjaa.97.010","url":null,"abstract":"Stembridge characterizes regular crystals associated with a simply-laced GCM in terms of local graph-theoretic quantities. We give a similar axiomatization for $B_2$ regular crystals (and thus for regular crystals of finite GCM except $G_2$ and affine GCM except $A^{(1)}_{1},G^{(1)}_{2},A^{(2)}_{2},D^{(3)}_4$). Our motivation comes from a generalization of Schur partition theorem by the author jointly with Masaki Watanabe proved indirectly via theory of perfect crystal.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2017-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74736112","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 formulate the notion of an isomorphism of GKM graphs. We then show that two GKM graphs have isomorphic graph equivariant cohomology algebras if and only if the graphs are isomorphic.
给出了GKM图的同构概念。然后我们证明两个GKM图有同构图等变上同调代数当且仅当这两个图同构。
{"title":"Graph equivariant cohomological rigidity for GKM graphs","authors":"M. Franz, H. Yamanaka","doi":"10.3792/pjaa.95.107","DOIUrl":"https://doi.org/10.3792/pjaa.95.107","url":null,"abstract":"We formulate the notion of an isomorphism of GKM graphs. We then show that two GKM graphs have isomorphic graph equivariant cohomology algebras if and only if the graphs are isomorphic.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2017-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85907685","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 construct an infinite family of elliptic curves whose rank is exactly two and the torsion subgroup is a cyclic group of order two or three, under the parity conjecture.
在宇称猜想下，构造了秩为二的椭圆曲线无穷族，其扭转子群为二阶或三阶的循环群。
{"title":"Infinitely many elliptic curves of rank exactly two II","authors":"Keunyoung Jeong","doi":"10.3792/PJAA.95.53","DOIUrl":"https://doi.org/10.3792/PJAA.95.53","url":null,"abstract":"In this paper, we construct an infinite family of elliptic curves whose rank is exactly two and the torsion subgroup is a cyclic group of order two or three, under the parity conjecture.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2016-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91076206","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 : 2015-10-31DOI: 10.4134/CKMS.2015.30.4.379
D. Jeon
In this paper, we find all Weierstrass points on the hyperelliptic modular curves X0ðNÞ whose hyperelliptic involutions are non-exceptional, i.e., induced by matrices in GL2ðRÞ.
{"title":"Weierstrass points on hyperelliptic modular curves","authors":"D. Jeon","doi":"10.4134/CKMS.2015.30.4.379","DOIUrl":"https://doi.org/10.4134/CKMS.2015.30.4.379","url":null,"abstract":"In this paper, we find all Weierstrass points on the hyperelliptic modular curves X0ðNÞ whose hyperelliptic involutions are non-exceptional, i.e., induced by matrices in GL2ðRÞ.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2015-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75046567","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 prove that the graded ring of modular forms of weight divisible by 3 is naturally isomorphic to a certain log canonical ring of the corresponding elliptic modular surface.
证明了权可被3整除的模形式的分级环与相应的椭圆模曲面的某个对数正则环是自然同构的。
{"title":"Modular forms of weight $3m$ and elliptic modular surfaces","authors":"Shouhei Ma","doi":"10.3792/PJAA.95.31","DOIUrl":"https://doi.org/10.3792/PJAA.95.31","url":null,"abstract":"We prove that the graded ring of modular forms of weight divisible by 3 is naturally isomorphic to a certain log canonical ring of the corresponding elliptic modular surface.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2015-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72906354","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 work we study the problem of existence of symplectic structures on free nilpotent Lie algebras. Necessary and sufficient conditions are given for even dimensional ones. The one dimensional central extension for odd dimensional free nilpotent Lie algebras is also considered.
{"title":"Symplectic structures on free nilpotent Lie algebras","authors":"V. Barco","doi":"10.3792/pjaa.95.88","DOIUrl":"https://doi.org/10.3792/pjaa.95.88","url":null,"abstract":"In this work we study the problem of existence of symplectic structures on free nilpotent Lie algebras. Necessary and sufficient conditions are given for even dimensional ones. The one dimensional central extension for odd dimensional free nilpotent Lie algebras is also considered.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2011-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73632651","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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