Kyushu Journal of Mathematics最新文献

{"title":"WHITNEY APPROXIMATION FOR SMOOTH CW COMPLEX","authors":"Norio Iwase","doi":"10.2206/kyushujm.76.177","DOIUrl":"https://doi.org/10.2206/kyushujm.76.177","url":null,"abstract":"Theorem A.1 in [II19] claimed that a topological CW complex is homotopy equivalent to a smooth CW complex without details. To give a more precise proof, we show a version of Whitney Approximation for a smooth CW complex, which actually enables us to give a concrete proof for Theorem A.1 in [II19].","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49204437","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":"REMARKS ON DIMENSION OF HOMOLOGY SPHERES WITH ODD NUMBERS OF FIXED POINTS OF FINITE GROUP ACTIONS","authors":"S. Tamura","doi":"10.2206/kyushujm.74.255","DOIUrl":"https://doi.org/10.2206/kyushujm.74.255","url":null,"abstract":"For each positive integer m, an arbitrary finite non-solvable group acts smoothly on infinitely many standard spheres with exactly m fixed points. However, for a given finite non-solvable group G and a given positive integer m, all standard spheres do not admit smooth actions of G with exactly m fixed points. In this paper, for each of the alternating group A6 on six letters, the symmetric group S6 on six letters, the projective general linear group PGL(2, 9) of order 720, the Mathieu group M10 of order 720, the automorphism group Aut(A6) of A6 and the special linear group SL(2, 9) of order 720, we will give the dimensions of homology spheres whose fixed point sets of smooth actions of the group do not consist of odd numbers of points.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68557027","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":"OKADA'S THEOREM AND MULTIPLE DIRICHLET SERIES","authors":"Y. Hamahata","doi":"10.2206/kyushujm.74.429","DOIUrl":"https://doi.org/10.2206/kyushujm.74.429","url":null,"abstract":"Let k1, . . . , kr be positive integers. Let q1, . . . , qr be pairwise coprime positive integers with qi > 2 (i = 1, . . . , r ), and set q = q1 · · · qr . For each i = 1, . . . , r , let Ti be a set of φ(qi )/2 representatives mod qi such that the union Ti ∪ (−Ti ) is a complete set of coprime residues mod qi . Let K be an algebraic number field over which the qth cyclotomic polynomial 8q is irreducible. Then, φ(q)/2r numbers r ∏ i=1 dki−1 dzi i (cot π zi )|zi=ai /qi (ai ∈ Ti , i = 1, . . . , r) are linearly independent over K . As an application, a generalization of the Baker–Birch– Wirsing theorem on the non-vanishing of the multiple Dirichlet series L(s1, . . . , sr ; f ) with periodic coefficients at (s1, . . . , sr )= (k1, . . . , kr ) is proven under a parity condition.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68557468","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 BOUNDARY LERCH ZETA-FUNCTION AND SHORT CHARACTER SUMS À LA Y. YAMAMOTO","authors":"Xiaohan-H. Wang, J. Mehta, S. Kanemitsu","doi":"10.2206/kyushujm.74.313","DOIUrl":"https://doi.org/10.2206/kyushujm.74.313","url":null,"abstract":". As has been pointed out by Chakraborty et al (Seeing the invisible: around generalized Kubert functions. Ann. Univ. Sci. Budapest. Sect. Comput. 47 (2018), 185–195), there have appeared many instances in which only the imaginary part—the odd part—of the Lerch zeta-function was considered by eliminating the real part. In this paper we shall make full use of (the boundary function aspect of) the q -expansion for the Lerch zeta-function, the boundary function being in the sense of Wintner (On Riemann’s fragment concerning elliptic modular functions. Amer. J. Math. 63 (1941), 628–634). We may thus refer to this as the ‘Fourier series–boundary q -series’, and we shall show that the decisive result of Yamamoto (Dirichlet series with periodic coefficients. Algebraic Number Theory. Japan Society for the Promotion of Science, Tokyo, 1977, pp. 275–289) on short character sums is its natural consequence. We shall also elucidate the aspect of generalized Euler constants as Laurent coefficients after a brief introduction of the discrete Fourier transform. These are rather remote consequences of the modular relation, i.e. the functional equation for the Lerch zeta-function or the polylogarithm function. That such a remote-looking subject as short character sums is, in the long run, also a consequence of the functional equation indicates the ubiquity and omnipotence of the Lerch zeta-function—and, a fortiori , the modular relation (S. Kanemitsu and H. Tsukada. Contributions to the Theory of Zeta-Functions: the Modular Relation Supremacy. World Scientific, Singapore, 2014). (1.6), the Lerch zeta-function (1.4) is less well known, the existing monograph [ 36 ] notwithstanding. Recently there has been a new representation-theoretic interpretation of the Lerch zeta-function, cf. e.g. [ 35 ]. In the last few decades, the most fundamental and influential works related to the Lerch zeta-function are [ 16 ], [ 43 ], [ 47 ], and [ 71 ], which are partly incorporated in [ 10 ]. We shall describe these toward the end of this section. In the paper [ 9 ] the ubiquity of the Lerch zeta-function, especially the monologarithm (cid:96) 1 ( x ) (1.22) of the complex exponential argument, has been pursued.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68557660","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":"INHOMOGENEOUS DIRICHLET-BOUNDARY VALUE PROBLEM FOR TWO-DIMENSIONAL QUADRATIC NONLINEAR SCHRÖDINGER EQUATIONS","authors":"N. Hayashi, E. Kaikina","doi":"10.2206/kyushujm.74.375","DOIUrl":"https://doi.org/10.2206/kyushujm.74.375","url":null,"abstract":"We consider the inhomogeneous Dirichlet–boundary value problem for the quadratic nonlinear Schrödinger equations, which is considered as a critical case for the largetime asymptotics of solutions. We present sufficient conditions on the initial and boundary data which ensure asymptotic behavior of small solutions to the equations by using the classical energy method and factorization techniques of the free Schrödinger group.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68557763","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":"L1-DETERMINED PRIMITIVE IDEALS IN THE C∗-ALGEBRA OF AN EXPONENTIAL LIE GROUP WITH CLOSED NON-∗-REGULAR ORBITS","authors":"Junko Inoue, J. Ludwig","doi":"10.2206/kyushujm.74.127","DOIUrl":"https://doi.org/10.2206/kyushujm.74.127","url":null,"abstract":"Let G = exp(g) be an exponential solvable Lie group and Ad(G)⊂ D an exponential solvable Lie group of automorphisms of G. Assume that for every non-∗-regular orbit D · q, q ∈ g, of D= exp(d) in g, there exists a nilpotent ideal n of g containing d · g such that D · q|n is closed in n. We then show that for every D-orbit  in g the kernel kerC∗() of  in the C-algebra of G is L1-determined, which means that kerC∗() is the closure of the kernel kerL1() of  in the group algebra L 1(G). This establishes also a new proof of a result of Ungermann, who obtained the same result for the trivial group D= Ad(G). We finally give an example of a non-closed non-∗-regular orbit of an exponential solvable group G and of a coadjoint orbit O ⊂ g, for which the corresponding kernel kerC∗(πO) in C(G) is not L1-determined.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68557088","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":"TWISTED ALEXANDER POLYNOMIAL AND MATRIX-WEIGHTED ZETA FUNCTION","authors":"H. Goda","doi":"10.2206/kyushujm.74.211","DOIUrl":"https://doi.org/10.2206/kyushujm.74.211","url":null,"abstract":". The twisted Alexander polynomial is an invariant of the pair of a knot and its group representation. Herein, we introduce a digraph obtained from an oriented knot diagram, which is used to study the twisted Alexander polynomial of knots. In this context, we show that the inverse of the twisted Alexander polynomial of a knot may be regarded as the matrix-weighted zeta function that is a generalization of the Ihara–Selberg zeta function of a directed weighted graph.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"53 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68557386","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 C* -ALGEBRAS OF SEMI-DIRECT PRODUCTS OF FINITE CYCLIC GROUPS BY K-THEORY","authors":"Takahiro Sudo","doi":"10.2206/kyushujm.74.223","DOIUrl":"https://doi.org/10.2206/kyushujm.74.223","url":null,"abstract":"We study some finite discrete groups such as semi-direct products of finite cyclic groups by their automorphisms, the corresponding group and subgroup C-algebras, and their K-theory. Consequently, we obtain several isomorphism classification theorems of such groups by their group C-algebras and K-theory.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68556947","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 MEAN SQUARE OF THE LOGARITHMIC DERIVATIVE OF THE SELBERG ZETA FUNCTION FOR COCOMPACT DISCRETE SUBGROUPS","authors":"Y. Aoki","doi":"10.2206/kyushujm.74.353","DOIUrl":"https://doi.org/10.2206/kyushujm.74.353","url":null,"abstract":"","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"74 1","pages":"353-373"},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68557738","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 THE ASYMPTOTIC EXPANSION OF THE QUANTUM SU(2) INVARIANT AT ζ = e4πi/r FOR LENS SPACE L (p, q)","authors":"T. Takata, Rika Tanaka","doi":"10.2206/kyushujm.74.265","DOIUrl":"https://doi.org/10.2206/kyushujm.74.265","url":null,"abstract":"We give a formula for the quantum SU(2) invariant at ζ = e4π i/r for Lens space L(p, q), and we prove that the asymptotic expansion is represented by a sum of contributions from SL2C flat connections whose coefficients are square roots of the Reidemeister torsions.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.4,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68557643","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}