For each prime p, we give an upper bound in m for Poincaré series Pþ k ðz;mÞ of weight k for 0 ðpÞ to be non-vanishing.
对于每一个素数p，我们给出了权值k为0 ðpÞ的poincar级数Pþ k ðz;mÞ在m中的一个不消失的上界。
{"title":"A note on the non-vanishing of Poincaré series for the Fricke group $Gamma_{0}^{+}(p)$","authors":"Soyoung Choi, Bo-Hae Im","doi":"10.3792/PJAA.95.24","DOIUrl":"https://doi.org/10.3792/PJAA.95.24","url":null,"abstract":"For each prime p, we give an upper bound in m for Poincaré series Pþ k ðz;mÞ of weight k for 0 ðpÞ to be non-vanishing.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86878137","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 log Iitaka conjecture holds for log canonical fibrations when log canonical divisor of a sufficiently general fiber is abundant.
我们证明了当足够一般的纤维的对数正则因子丰富时，对数Iitaka猜想对对数正则纤维成立。
{"title":"Log Iitaka conjecture for abundant log canonical fibrations","authors":"K. Hashizume","doi":"10.3792/pjaa.96.017","DOIUrl":"https://doi.org/10.3792/pjaa.96.017","url":null,"abstract":"We prove that the log Iitaka conjecture holds for log canonical fibrations when log canonical divisor of a sufficiently general fiber is abundant.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82423240","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 give a classification of irreducible symmetric spaces which admit standard compact Clifford–Klein forms. The method uses representation theory over the real number field and the criterion for properness and cocompactness of the action on homogeneous spaces due to T. Kobayashi.
{"title":"Classification of irreducible symmetric spaces which admit standard compact Clifford–Klein forms","authors":"Koichi Tojo","doi":"10.3792/PJAA.95.11","DOIUrl":"https://doi.org/10.3792/PJAA.95.11","url":null,"abstract":": We give a classification of irreducible symmetric spaces which admit standard compact Clifford–Klein forms. The method uses representation theory over the real number field and the criterion for properness and cocompactness of the action on homogeneous spaces due to T. Kobayashi.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85866014","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":"Hypertranscendence of the multiple sine function for a complex period","authors":"Masakimi Kato","doi":"10.3792/pjaa.95.16","DOIUrl":"https://doi.org/10.3792/pjaa.95.16","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76352640","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":"The number of orientable small covers over a product of simplices","authors":"Murat Altunbulak, A. Ilhan","doi":"10.3792/pjaa.95.1","DOIUrl":"https://doi.org/10.3792/pjaa.95.1","url":null,"abstract":"","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78275042","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 Stieltjes constants $gamma_n(K)$ of a number field $K$ are the coefficients of the Laurent expansion of the Dedekind zeta function $zeta_K(s)$ at its pole $s=1$. In this paper, we establish a similar expression of $gamma_n(K)$ as Stieltjes obtained in 1885 for $gamma_n(mathbb Q)$. We also study the signs of $gamma_n(K)$.
{"title":"The signs of the Stieltjes constants associated with the Dedekind zeta function","authors":"Sumaia Saad Eddin","doi":"10.3792/pjaa.94.93","DOIUrl":"https://doi.org/10.3792/pjaa.94.93","url":null,"abstract":"The Stieltjes constants $gamma_n(K)$ of a number field $K$ are the coefficients of the Laurent expansion of the Dedekind zeta function $zeta_K(s)$ at its pole $s=1$. In this paper, we establish a similar expression of $gamma_n(K)$ as Stieltjes obtained in 1885 for $gamma_n(mathbb Q)$. We also study the signs of $gamma_n(K)$.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74686771","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}
T. Miezaki, M. Oura, Tadashi Sakuma, Hidehiro Shinohara
In this paper, we introduce the concept of the Tutte polynomials of genus $g$ and discuss some of its properties. We note that the Tutte polynomials of genus one are well-known Tutte polynomials. The Tutte polynomials are matroid invariants, and we claim that the Tutte polynomials of genus $g$ are also matroid invariants. The main result of this paper and the forthcoming paper declares that the Tutte polynomials of genus $g$ are complete matroid invariants.
{"title":"A generalization of the Tutte polynomials","authors":"T. Miezaki, M. Oura, Tadashi Sakuma, Hidehiro Shinohara","doi":"10.3792/pjaa.95.111","DOIUrl":"https://doi.org/10.3792/pjaa.95.111","url":null,"abstract":"In this paper, we introduce the concept of the Tutte polynomials of genus $g$ and discuss some of its properties. We note that the Tutte polynomials of genus one are well-known Tutte polynomials. The Tutte polynomials are matroid invariants, and we claim that the Tutte polynomials of genus $g$ are also matroid invariants. The main result of this paper and the forthcoming paper declares that the Tutte polynomials of genus $g$ are complete matroid invariants.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88346617","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 an odd prime p, it is shown that if G 1⁄4 AB is a finite p-group, for subgroups A and B such that A is cyclic and B is abelian of exponent at most p, then kðAÞB E G, where kðAÞ 1⁄4 hg 2 A j g k 1⁄4 1i.
对于奇素数p，证明了如果G 1 / 4 AB是有限p群，对于子群a和B，使得a是循环的，B是幂次的不超过p的，则kðAÞB E G，其中kðAÞ 1 / 4 hg 2 a j G k 1 / 4 1i。
{"title":"On products of cyclic and abelian finite $p$-groups ($ p$ odd)","authors":"B. McCann","doi":"10.3792/pjaa.94.77","DOIUrl":"https://doi.org/10.3792/pjaa.94.77","url":null,"abstract":"For an odd prime p, it is shown that if G 1⁄4 AB is a finite p-group, for subgroups A and B such that A is cyclic and B is abelian of exponent at most p, then kðAÞB E G, where kðAÞ 1⁄4 hg 2 A j g k 1⁄4 1i.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89075811","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 that the fundamental group of the $3$-manifold obtained by $frac{p}{q}$-surgery along the $(n-2)$-twisted $(3,3m+2)$-torus knot, with $n,m ge 1$, is not left-orderable if $frac{p}{q} ge 2n + 6m-3$ and is left-orderable if $frac{p}{q}$ is sufficiently close to $0$.
我们证明了基群 $3$-流形由 $frac{p}{q}$-手术沿 $(n-2)$扭曲的 $(3,3m+2)$-环结，带 $n,m ge 1$，是不可左序的 $frac{p}{q} ge 2n + 6m-3$ 它是左序的，如果 $frac{p}{q}$ 足够接近 $0$．
{"title":"Left-orderability for surgeries on twisted torus knots","authors":"Anh T. Tran","doi":"10.3792/PJAA.95.6","DOIUrl":"https://doi.org/10.3792/PJAA.95.6","url":null,"abstract":"We show that the fundamental group of the $3$-manifold obtained by $frac{p}{q}$-surgery along the $(n-2)$-twisted $(3,3m+2)$-torus knot, with $n,m ge 1$, is not left-orderable if $frac{p}{q} ge 2n + 6m-3$ and is left-orderable if $frac{p}{q}$ is sufficiently close to $0$.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87007332","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 consider the order of holomorphic curves with maximal deficiency sum in the complex plane. The purpose of this paper is to weaken the condition treated in the paper [9]. As a special case we obtain the result in [9].
{"title":"On the order of holomorphic curves with maximal deficiency sum, II","authors":"Nobushige Toda","doi":"10.2996/KMJ/1138043483","DOIUrl":"https://doi.org/10.2996/KMJ/1138043483","url":null,"abstract":": In this paper we consider the order of holomorphic curves with maximal deficiency sum in the complex plane. The purpose of this paper is to weaken the condition treated in the paper [9]. As a special case we obtain the result in [9].","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89460847","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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