Kyushu Journal of Mathematics最新文献

{"title":"HYPERGEOMETRY INSPIRED BY IRRATIONALITY QUESTIONS","authors":"C. Krattenthaler, W. Zudilin","doi":"10.2206/kyushujm.73.189","DOIUrl":"https://doi.org/10.2206/kyushujm.73.189","url":null,"abstract":"We report new hypergeometric constructions of rational approximations to Catalan's constant, $log2$, and $pi^2$, their connection with already known ones, and underlying `permutation group' structures. Our principal arithmetic achievement is a new partial irrationality result for the values of Riemann's zeta function at odd integers.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2206/kyushujm.73.189","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48528700","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":"ON MELLIN-BARNES INTEGRAL REPRESENTATIONS FOR GKZ HYPERGEOMETRIC FUNCTIONS","authors":"Saiei-Jaeyeong Matsubara-Heo","doi":"10.2206/kyushujm.74.109","DOIUrl":"https://doi.org/10.2206/kyushujm.74.109","url":null,"abstract":"We consider Mellin-Barnes integral representations of GKZ hypergeometric equations. We construct integration contours in an explicit way and show that suitable analytic continuations give rise to a basis of solutions.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44410309","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":"ROOTED TREE MAPS AND THE KAWASHIMA RELATIONS FOR MULTIPLE ZETA VALUES","authors":"Henrik Bachmann, Tatsushi Tanaka","doi":"10.2206/kyushujm.74.169","DOIUrl":"https://doi.org/10.2206/kyushujm.74.169","url":null,"abstract":"Recently, inspired by the Connes-Kreimer Hopf algebra of rooted trees, the second named author introduced rooted tree maps as a family of linear maps on the noncommutative polynomial algebra in two letters. These give a class of relations among multiple zeta values, which are known to be a subclass of the so-called linear part of the Kawashima relations. In this paper we show the opposite implication, that is the linear part of the Kawashima relations is implied by the relations coming from rooted tree maps.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48124147","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":"ABSOLUTE CONTINUITY FOR UNBOUNDED POSITIVE SELF-ADJOINT OPERATORS","authors":"H. Kosaki","doi":"10.2206/KYUSHUJM.72.407","DOIUrl":"https://doi.org/10.2206/KYUSHUJM.72.407","url":null,"abstract":"The notion of absolute continuity for positive operators was studied by T. Ando, where parallel sums for such operators played an important role. On the other hand, a theory for parallel sums for densely defined positive self-adjoint operators (or more generally positive forms) was developed in our previous work. Based on this theory, we will investigate the notion of absolute continuity in such unbounded cases.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"72 1","pages":"407-421"},"PeriodicalIF":0.4,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2206/KYUSHUJM.72.407","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68555791","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":"AN APPLICATION OF GENERALIZED MOLLIFIERS TO THE RIEMANN ZETA-FUNCTION","authors":"Keiju Sono","doi":"10.2206/KYUSHUJM.72.35","DOIUrl":"https://doi.org/10.2206/KYUSHUJM.72.35","url":null,"abstract":"In this paper, we establish the asymptotic formula for the second moment of the Riemann zeta-function twisted by a (3+ 1)-piece mollifier which is a generalization of the two-piece mollifier considered by Bui, Conrey and Young [Acta. Arith. 150(1) (2011), 35–64]. As an application, we obtain a lower bound for the proportion of critical zeros of the Riemann zeta-function.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"7 1","pages":"35-69"},"PeriodicalIF":0.4,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2206/KYUSHUJM.72.35","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68555759","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 DETAILED STUDY OF THE RELATIONSHIP BETWEEN SOME OF THE ROOT LATTICES AND THE CODING THEORY","authors":"M. Ozeki","doi":"10.2206/KYUSHUJM.72.123","DOIUrl":"https://doi.org/10.2206/KYUSHUJM.72.123","url":null,"abstract":"Summary: In the present article we study the even unimodular lattice which lies between the root lattice m · A n and the dual lattice ( m · A n ) # . Here m · A n is an orthogonal sum of m copies of the root lattice A n . In the course of the study the code over the ring A # n /A n arises in a natural way. We find that an intimate relationship between the even unimodular lattice containing m · A n as a sublattice and the error correcting code over the ring A # n /A n exists. As a consequence we could reconstruct sixteen non-isometric Niemeier lattices out of twenty-four non-isometric lattices by using the present approach.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"12 1","pages":"123-141"},"PeriodicalIF":0.4,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68555003","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":"RAMIFICATION OVER HYPERSURFACES LOCATED IN SUBGENERAL POSITION OF THE GAUSS MAP OF COMPLETE MINIMAL SURFACES WITH FINITE TOTAL CURVATURE","authors":"D. D. Thai, Pham Duc Thoan","doi":"10.2206/KYUSHUJM.72.253","DOIUrl":"https://doi.org/10.2206/KYUSHUJM.72.253","url":null,"abstract":"The first aim of this paper is to show the second main theorem for holomorphic maps from a compact Riemann surface into the complex projective space which is ramified over hypersurfaces in subgeneral position. We then use it to study the ramification over hypersurfaces of the generalized Gauss map of complete regular minimal surfaces in Rm with finite total curvature, sharing hypersurfaces in subgeneral position. The results generalize our previous results [Thai and Thoan, Vietnam J. Math. 2017, doi:10.1007/s10013-017-0259-6].","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"9 1","pages":"253-267"},"PeriodicalIF":0.4,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2206/KYUSHUJM.72.253","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68555328","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":"COKERNELS OF HOMOMORPHISMS FROM BURNSIDE RINGS TO INVERSE LIMITS II: G = Cpm × Cpn","authors":"M. Morimoto, Masafumi Sugimura","doi":"10.2206/KYUSHUJM.72.95","DOIUrl":"https://doi.org/10.2206/KYUSHUJM.72.95","url":null,"abstract":"Let G be a finite group and A(G) the Burnside ring of G. The family of rings A(H), where H ranges over the set of all proper subgroups of G, yields the inverse limit L(G) and a canonical homomorphism from A(G) to L(G) which is called the restriction map. Let Q(G) be the cokernel of this homomorphism. It is known that Q(G) is a finite abelian group and is isomorphic to the cartesian product of Q(G/N (p)), where p runs over the set of primes dividing the order of G and N (p) stands for the smallest normal subgroup of G such that the order of G/N (p) is a power of p. Therefore, it is important to investigate Q(G) for G of prime power order. In this paper we develop a way to compute Q(G) for cartesian products G of two cyclic p-groups.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"72 1","pages":"95-105"},"PeriodicalIF":0.4,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68555428","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":"ESTIMATES FOR THE EIGENVALUES OF THE DRIFTING LAPLACIAN ON SOME COMPLETE RICCI SOLITONS","authors":"Lingzhong Zeng","doi":"10.2206/KYUSHUJM.72.143","DOIUrl":"https://doi.org/10.2206/KYUSHUJM.72.143","url":null,"abstract":"Ricci solitons are the self-similar solutions to the Ricci flow, which play an important role in understanding the singularity dilations of the Ricci flow. In this paper, we investigate eigenvalues of the Dirichlet problem of a drifting Laplacian on some important complete Ricci solitons: the product shrinking Ricci soliton, cigar soliton, and so on. Since eigenvalues are invariant of isometries, we can give the estimates for the eigenvalues of a drifting Laplacian on the rotationally invariant shrinking solitons. In addition, we also obtain a sharp upper bound of the kth eigenvalue of the a drifting Laplacian on the product Ricci soliton in the sense of order k.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"72 1","pages":"143-156"},"PeriodicalIF":0.4,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.2206/KYUSHUJM.72.143","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68555055","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":"Takeuchi’s equality for the levi form of the fubini–study distance to complex submanifolds in complex projective spaces","authors":"Kazuko Matsumoto","doi":"10.2206/KYUSHUJM.72.107","DOIUrl":"https://doi.org/10.2206/KYUSHUJM.72.107","url":null,"abstract":"A. Takeuchi showed that the negative logarithm of the Fubini–Study boundary distance function of pseudoconvex domains in the complex projective space CPn , n ∈ N, is strictly plurisubharmonic and solved the Levi problem for CPn . His estimate from below of the Levi form is nowadays called the ‘Takeuchi’s inequality.’ In this paper, we give the ‘Takeuchi’s equality,’ i.e. an explicit representation of the Levi form of the negative logarithm of the Fubini–Study distance to complex submanifolds in CPn . 0. Introduction Let D (CPn , n ∈ N, be a pseudoconvex domain and denote by δ∂D(P) the Fubini– Study distance from P ∈ D to the boundary ∂D of D. Takeuchi [21] found that the strict subharmonicity of the function −log tan−1|z| on C {0} leads the strict plurisubharmonicity of the function −log δ∂D on D, and solved the Levi problem for CPn . The inequality i∂∂̄(−log δ∂D)≥ 3ωF S on D is nowadays called the ‘Takeuchi’s inequality’ (cf. [1, 7, 9, 20, 22]). Recently, many mathematicians have been interested in the following problem: ‘Is there a smooth closed Levi-flat real hypersurface in CPn if n ≥ 2?’, where a real hypersurface M ⊂ CPn is said to be Levi-flat if its complement CPn M is locally pseudoconvex or equivalently locally Stein. When n ≥ 3, Lins Neto [11] proved the non-existence in the real analytic case, and Siu [19] proved it in the smooth case. When n = 2, the non-existence problem is still open even in the real analytic case. Then Takeuchi’s inequality is one of the key points to approach the non-existence problem or related topics. His paper [21] is frequently cited even now although he wrote it over 50 years ago (for example, see Adachi [1], Adachi and Brinkschulte [2], Brinkschulte [5], Brunella [6], Fu and Shaw [8], Harrington and Shaw [10], Ohsawa [16, 17], and Ohsawa and Sibony [18]). It follows from Takeuchi’s theorem that if S is a complex hypersurface in CPn and if δS denotes the Fubini–Study distance to S, then the function−log δS is strictly plurisubharmonic 2010 Mathematics Subject Classification: Primary 32E40, 32C25.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"72 1","pages":"107-121"},"PeriodicalIF":0.4,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68554978","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}