Kodai Mathematical Journal最新文献

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Structure of the associated groups of quandles 关联的量子群的结构
IF 0.6 4区 数学
Kodai Mathematical Journal Pub Date : 2022-06-30 DOI: 10.2996/kmj45205
Toshiyuki Akita, Aoi Hasegawa, Masayoshi Tanno
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引用次数: 1
Explicit estimates in inter-universal Teichmüller theory 泛间Teichmüller理论中的显式估计
IF 0.6 4区 数学
Kodai Mathematical Journal Pub Date : 2022-06-30 DOI: 10.2996/kmj45201
S. Mochizuki, I. Fesenko, Yuichiro Hoshi, Arata Minamide, Wojciech Porowski
{"title":"Explicit estimates in inter-universal Teichmüller theory","authors":"S. Mochizuki, I. Fesenko, Yuichiro Hoshi, Arata Minamide, Wojciech Porowski","doi":"10.2996/kmj45201","DOIUrl":"https://doi.org/10.2996/kmj45201","url":null,"abstract":"In the final paper of a series of papers concerning interuniversal Teichmüller theory, Mochizuki verified various numerically non-effective versions of the Vojta, ABC, and Szpiro Conjectures over number fields. In the present paper, we obtain various numerically effective versions of Mochizuki’s results. In order to obtain these results, we first establish a version of the theory of étale theta functions that functions properly at arbitrary bad places, i.e., even bad places that divide the prime “2”. We then proceed to discuss how such a modified version of the theory of étale theta functions affects inter-universal Teichmüller theory. Finally, by applying our slightly modified version of inter-universal Teichmüller theory, together with various explicit estimates concerning heights, the j-invariants of “arithmetic” elliptic curves, and the prime number theorem, we verify the numerically effective versions of Mochizuki’s results referred to above. These numerically effective versions imply effective diophantine results such as an effective version of the ABC inequality over mono-complex number fields [i.e., the rational number field or an imaginary quadratic field] and effective versions of conjectures of Szpiro. We also obtain an explicit estimate concerning “Fermat’s Last Theorem” (FLT) — i.e., to the effect that FLT holds for prime exponents > 1.615 · 10 — which is sufficient, in light of a numerical result of Coppersmith, to give an alternative proof of the first case of FLT. In the second case of FLT, if one combines the techniques of the present paper with a recent estimate due to Mihăilescu and Rassias, then the lower bound “1.615 · 10” can be improved to “257”. This estimate, combined with a classical result of Vandiver, yields an alternative proof of the second case of FLT. In particular, the results of the present paper, combined with the results of Vandiver, Coppersmith, and Mihăilescu-Rassias, yield an unconditional new alternative proof of Fermat’s Last Theorem.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44496933","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}
引用次数: 1
On complete hypersurfaces with constant scalar curvature $n(n-1)$ in the unit sphere 单位球面上常标曲率为$n(n-1)$的完备超曲面
IF 0.6 4区 数学
Kodai Mathematical Journal Pub Date : 2022-05-26 DOI: 10.2996/kmj46104
Jinchuan Bai, Yong Luo
{"title":"On complete hypersurfaces with constant scalar curvature $n(n-1)$ in the unit sphere","authors":"Jinchuan Bai, Yong Luo","doi":"10.2996/kmj46104","DOIUrl":"https://doi.org/10.2996/kmj46104","url":null,"abstract":"Let $M^n$ be an $n$-dimensional complete and locally conformally flat hypersurface in the unit sphere $mathbb{S}^{n+1}$ with constant scalar curvature $n(n-1)$. We show that if the total curvature $left( int _ { M } | H | ^ { n } d v right) ^ { frac { 1 } { n } }$ of $M$ is sufficiently small, then $M^n$ is totally geodesic.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42709300","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}
引用次数: 0
Local normal forms of em-wavefronts in affine flat coordinates 仿射平面坐标中em波前的局部正规形式
IF 0.6 4区 数学
Kodai Mathematical Journal Pub Date : 2022-04-28 DOI: 10.2996/kmj45305
Naomichi Nakajima
{"title":"Local normal forms of em-wavefronts in affine flat coordinates","authors":"Naomichi Nakajima","doi":"10.2996/kmj45305","DOIUrl":"https://doi.org/10.2996/kmj45305","url":null,"abstract":". In our previous work, we have generalized the notion of dually flat or Hessian manifold to quasi-Hessian manifold ; it admits the Hessian metric to be degenerate but possesses a particular symmetric cubic tensor (generalized Amari-Centsov tensor). Indeed, it naturally appears as a singular model in information geometry and related fields. A quasi-Hessian manifold is locally accompanied with a possibly multi-valued potential and its dual, whose graphs are called the e -wavefront and the m -wavefront respectively, together with coherent tangent bundles endowed with flat connections. In the present paper, using those connections and the metric, we give coordinate-free criteria for detecting local diffeomorphic types of e/m -wavefronts, and then derive the local normal forms of those (dual) potential functions for the e/m -wavefronts in affine flat coordinates by means of Malgrange’s division theorem. This is motivated by an early work of Ekeland on non-convex optimization and Saji-Umehara-Yamada’s work on Riemannian geometry of wavefronts. Finally, we reveal a relation of our geometric criteria with information geometric quantities of statistical manifolds.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41660268","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}
引用次数: 0
Estimates for the higher eigenvalues of the drifting Laplacian on Hadamard manifolds Hadamard流形上漂移拉普拉斯算子高本征值的估计
IF 0.6 4区 数学
Kodai Mathematical Journal Pub Date : 2022-03-18 DOI: 10.2996/kmj/kmj45109
Xin Xiong, Lingzhong Zeng, Huihui Zhu
{"title":"Estimates for the higher eigenvalues of the drifting Laplacian on Hadamard manifolds","authors":"Xin Xiong, Lingzhong Zeng, Huihui Zhu","doi":"10.2996/kmj/kmj45109","DOIUrl":"https://doi.org/10.2996/kmj/kmj45109","url":null,"abstract":"","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46588617","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}
引用次数: 1
Construction of Non-$timesmu$-Indivisible TKND-AVKF-fields 非$ $倍$ $-不可分tknd - avkf域的构造
IF 0.6 4区 数学
Kodai Mathematical Journal Pub Date : 2022-03-18 DOI: 10.2996/kmj/kmj45103
Shota Tsujimura
{"title":"Construction of Non-$timesmu$-Indivisible TKND-AVKF-fields","authors":"Shota Tsujimura","doi":"10.2996/kmj/kmj45103","DOIUrl":"https://doi.org/10.2996/kmj/kmj45103","url":null,"abstract":"","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41334865","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}
引用次数: 2
On the dimension of the global sections of adjoint bundles for quasi-polarized manifold whose anti-canonical bundle is effective, nef and big 拟极化流形的伴随束整体截面的维数,其反正则束是有效的、nef的和大的
IF 0.6 4区 数学
Kodai Mathematical Journal Pub Date : 2022-03-18 DOI: 10.2996/kmj/kmj45101
Y. Fukuma
{"title":"On the dimension of the global sections of adjoint bundles for quasi-polarized manifold whose anti-canonical bundle is effective, nef and big","authors":"Y. Fukuma","doi":"10.2996/kmj/kmj45101","DOIUrl":"https://doi.org/10.2996/kmj/kmj45101","url":null,"abstract":"","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44649745","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}
引用次数: 0
On adjoint torsion polynomial of genus one two-bridge knots 关于亏格一二桥节点的伴随扭转多项式
IF 0.6 4区 数学
Kodai Mathematical Journal Pub Date : 2022-03-18 DOI: 10.2996/kmj/kmj45107
Takayuki Morifuji
{"title":"On adjoint torsion polynomial of genus one two-bridge knots","authors":"Takayuki Morifuji","doi":"10.2996/kmj/kmj45107","DOIUrl":"https://doi.org/10.2996/kmj/kmj45107","url":null,"abstract":"","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42719720","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}
引用次数: 1
Mixed commutator lengths, wreath products and general ranks 混合换向器长度、环形产品和一般等级
IF 0.6 4区 数学
Kodai Mathematical Journal Pub Date : 2022-03-08 DOI: 10.2996/kmj46202
Morimichi Kawasaki, M. Kimura, Shuhei Maruyama, Takahiro Matsushita, M. Mimura
{"title":"Mixed commutator lengths, wreath products and general ranks","authors":"Morimichi Kawasaki, M. Kimura, Shuhei Maruyama, Takahiro Matsushita, M. Mimura","doi":"10.2996/kmj46202","DOIUrl":"https://doi.org/10.2996/kmj46202","url":null,"abstract":"In the present paper, for a pair $(G,N)$ of a group $G$ and its normal subgroup $N$, we consider the mixed commutator length $mathrm{cl}_{G,N}$ on the mixed commutator subgroup $[G,N]$. We focus on the setting of wreath products: $ (G,N)=(mathbb{Z}wr Gamma, bigoplus_{Gamma}mathbb{Z})$. Then we determine mixed commutator lengths in terms of the general rank in the sense of Malcev. As a byproduct, when an abelian group $Gamma$ is not locally cyclic, the ordinary commutator length $mathrm{cl}_G$ does not coincide with $mathrm{cl}_{G,N}$ on $[G,N]$ for the above pair. On the other hand, we prove that if $Gamma$ is locally cyclic, then for every pair $(G,N)$ such that $1to Nto Gto Gamma to 1$ is exact, $mathrm{cl}_{G}$ and $mathrm{cl}_{G,N}$ coincide on $[G,N]$. We also study the case of permutational wreath products when the group $Gamma$ belongs to a certain class related to surface groups.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44117954","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}
引用次数: 2
On the maximality of hyperelliptic Howe curves of genus 3 关于亏格3的超椭圆Howe曲线的极大性
IF 0.6 4区 数学
Kodai Mathematical Journal Pub Date : 2021-12-21 DOI: 10.2996/kmj45206
R. Ohashi
{"title":"On the maximality of hyperelliptic Howe curves of genus 3","authors":"R. Ohashi","doi":"10.2996/kmj45206","DOIUrl":"https://doi.org/10.2996/kmj45206","url":null,"abstract":"In this paper, we study a Howe curve C in positive characteristic p ≥ 3 which is of genus 3 and is hyperelliptic. We will show that if C is superspecial, then its standard form is maximal or minimal over Fp2 without taking its Fp2 -form.","PeriodicalId":54747,"journal":{"name":"Kodai Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47469457","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}
引用次数: 2
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