Pub Date : 2021-08-01DOI: 10.1017/s1446788720000312
{"title":"JAZ volume 111 issue 1 Cover and Front matter","authors":"","doi":"10.1017/s1446788720000312","DOIUrl":"https://doi.org/10.1017/s1446788720000312","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"16 1","pages":"f1 - f2"},"PeriodicalIF":0.7,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84417652","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 : 2021-07-18DOI: 10.1017/S1446788723000083
A. Varchenko, W. Zudilin
We prove general Dwork-type congruences for constant terms attached to tuples of Laurent polynomials. We apply this result to establishing arithmetic and p-adic analytic properties of functions originating from polynomial solutions modulo $p^s$ of hypergeometric and Knizhnik–Zamolodchikov (KZ) equations, solutions which come as coefficients of master polynomials and whose coefficients are integers. As an application, we show that the simplest example of a p-adic KZ connection has an invariant line subbundle while its complex analog has no nontrivial subbundles due to the irreducibility of its monodromy representation.
{"title":"GHOSTS AND CONGRUENCES FOR -APPROXIMATIONS OF HYPERGEOMETRIC PERIODS","authors":"A. Varchenko, W. Zudilin","doi":"10.1017/S1446788723000083","DOIUrl":"https://doi.org/10.1017/S1446788723000083","url":null,"abstract":"\u0000 We prove general Dwork-type congruences for constant terms attached to tuples of Laurent polynomials. We apply this result to establishing arithmetic and p-adic analytic properties of functions originating from polynomial solutions modulo \u0000 \u0000 \u0000 \u0000$p^s$\u0000\u0000 \u0000 of hypergeometric and Knizhnik–Zamolodchikov (KZ) equations, solutions which come as coefficients of master polynomials and whose coefficients are integers. As an application, we show that the simplest example of a p-adic KZ connection has an invariant line subbundle while its complex analog has no nontrivial subbundles due to the irreducibility of its monodromy representation.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"20 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2021-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87332550","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 : 2021-06-22DOI: 10.1017/S1446788721000100
Yongyang Jin, Shoufeng Shen
Abstract In this paper we obtain some improved $L^p$ -Hardy and $L^p$ -Rellich inequalities on bounded domains of Riemannian manifolds. For Cartan–Hadamard manifolds we prove the inequalities with sharp constants and with weights being hyperbolic functions of the Riemannian distance.
{"title":"SOME \u0000$boldsymbol {L^p}$\u0000 -HARDY AND \u0000$boldsymbol {L^p}$\u0000 -RELLICH TYPE INEQUALITIES WITH REMAINDER TERMS","authors":"Yongyang Jin, Shoufeng Shen","doi":"10.1017/S1446788721000100","DOIUrl":"https://doi.org/10.1017/S1446788721000100","url":null,"abstract":"Abstract In this paper we obtain some improved \u0000$L^p$\u0000 -Hardy and \u0000$L^p$\u0000 -Rellich inequalities on bounded domains of Riemannian manifolds. For Cartan–Hadamard manifolds we prove the inequalities with sharp constants and with weights being hyperbolic functions of the Riemannian distance.","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"3 1","pages":"79 - 98"},"PeriodicalIF":0.7,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86688076","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 : 2021-06-14DOI: 10.1017/S1446788722000209
J. M. Davies
Abstract Homotopy theory folklore tells us that the sheaf defining the cohomology theory $operatorname {mathrm {Tmf}}$ of topological modular forms is unique up to homotopy. Here we provide a proof of this fact, although we claim no originality for the statement. This retroactively reconciles all previous constructions of $operatorname {mathrm {Tmf}}$ .
{"title":"ELLIPTIC COHOMOLOGY IS UNIQUE UP TO HOMOTOPY","authors":"J. M. Davies","doi":"10.1017/S1446788722000209","DOIUrl":"https://doi.org/10.1017/S1446788722000209","url":null,"abstract":"Abstract Homotopy theory folklore tells us that the sheaf defining the cohomology theory \u0000$operatorname {mathrm {Tmf}}$\u0000 of topological modular forms is unique up to homotopy. Here we provide a proof of this fact, although we claim no originality for the statement. This retroactively reconciles all previous constructions of \u0000$operatorname {mathrm {Tmf}}$\u0000 .","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"24 1","pages":"99 - 118"},"PeriodicalIF":0.7,"publicationDate":"2021-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77625601","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 : 2021-06-01DOI: 10.1017/s1446788720000300
{"title":"JAZ volume 110 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s1446788720000300","DOIUrl":"https://doi.org/10.1017/s1446788720000300","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"14 1","pages":"b1 - b2"},"PeriodicalIF":0.7,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73102913","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 : 2021-06-01DOI: 10.1017/s1446788720000294
{"title":"JAZ volume 110 issue 3 Cover and Front matter","authors":"","doi":"10.1017/s1446788720000294","DOIUrl":"https://doi.org/10.1017/s1446788720000294","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"48 1","pages":"f1 - f2"},"PeriodicalIF":0.7,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73534984","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 : 2021-06-01DOI: 10.1017/s1446788718000587
{"title":"INDEX","authors":"","doi":"10.1017/s1446788718000587","DOIUrl":"https://doi.org/10.1017/s1446788718000587","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"1 1","pages":"431 - 432"},"PeriodicalIF":0.7,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73047095","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 : 2021-05-26DOI: 10.1017/S1446788722000040
Arnbjörg Soffía Árnadóttir, Waltraud Lederle, R. G. Möller
Abstract A connected, locally finite graph $Gamma $ is a Cayley–Abels graph for a totally disconnected, locally compact group G if G acts vertex-transitively on $Gamma $ with compact, open vertex stabilizers. Define the minimal degree of G as the minimal degree of a Cayley–Abels graph of G. We relate the minimal degree in various ways to the modular function, the scale function and the structure of compact open subgroups. As an application, we prove that if $T_{d}$ denotes the d-regular tree, then the minimal degree of $mathrm{Aut}(T_{d})$ is d for all $dgeq 2$ .
{"title":"CAYLEY–ABELS GRAPHS AND INVARIANTS OF TOTALLY DISCONNECTED, LOCALLY COMPACT GROUPS","authors":"Arnbjörg Soffía Árnadóttir, Waltraud Lederle, R. G. Möller","doi":"10.1017/S1446788722000040","DOIUrl":"https://doi.org/10.1017/S1446788722000040","url":null,"abstract":"Abstract A connected, locally finite graph \u0000$Gamma $\u0000 is a Cayley–Abels graph for a totally disconnected, locally compact group G if G acts vertex-transitively on \u0000$Gamma $\u0000 with compact, open vertex stabilizers. Define the minimal degree of G as the minimal degree of a Cayley–Abels graph of G. We relate the minimal degree in various ways to the modular function, the scale function and the structure of compact open subgroups. As an application, we prove that if \u0000$T_{d}$\u0000 denotes the d-regular tree, then the minimal degree of \u0000$mathrm{Aut}(T_{d})$\u0000 is d for all \u0000$dgeq 2$\u0000 .","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"44 1","pages":"145 - 177"},"PeriodicalIF":0.7,"publicationDate":"2021-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73470937","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 : 2021-05-12DOI: 10.1017/S1446788721000045
A. Brudnyi
Abstract Let $H^infty ({mathbb {D}}times {mathbb {N}})$ be the Banach algebra of bounded holomorphic functions defined on the disjoint union of countably many copies of the open unit disk ${mathbb {D}}subset {{mathbb C}}$ . We show that the dense stable rank of $H^infty ({mathbb {D}}times {mathbb {N}})$ is $1$ and, using this fact, prove some nonlinear Runge-type approximation theorems for $H^infty ({mathbb {D}}times {mathbb {N}})$ maps. Then we apply these results to obtain a priori uniform estimates of norms of approximating maps in similar approximation problems for the algebra $H^infty ({mathbb {D}})$ .
{"title":"DENSE STABLE RANK AND RUNGE-TYPE APPROXIMATION THEOREMS FOR \u0000${boldsymbol H}^{boldsymbol{infty}}$\u0000 MAPS","authors":"A. Brudnyi","doi":"10.1017/S1446788721000045","DOIUrl":"https://doi.org/10.1017/S1446788721000045","url":null,"abstract":"Abstract Let \u0000$H^infty ({mathbb {D}}times {mathbb {N}})$\u0000 be the Banach algebra of bounded holomorphic functions defined on the disjoint union of countably many copies of the open unit disk \u0000${mathbb {D}}subset {{mathbb C}}$\u0000 . We show that the dense stable rank of \u0000$H^infty ({mathbb {D}}times {mathbb {N}})$\u0000 is \u0000$1$\u0000 and, using this fact, prove some nonlinear Runge-type approximation theorems for \u0000$H^infty ({mathbb {D}}times {mathbb {N}})$\u0000 maps. Then we apply these results to obtain a priori uniform estimates of norms of approximating maps in similar approximation problems for the algebra \u0000$H^infty ({mathbb {D}})$\u0000 .","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"5 1","pages":"289 - 317"},"PeriodicalIF":0.7,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77001527","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 : 2021-04-01DOI: 10.1017/s1446788720000282
{"title":"JAZ volume 110 issue 2 Cover and Back matter","authors":"","doi":"10.1017/s1446788720000282","DOIUrl":"https://doi.org/10.1017/s1446788720000282","url":null,"abstract":"","PeriodicalId":50007,"journal":{"name":"Journal of the Australian Mathematical Society","volume":"95 1","pages":"b1 - b2"},"PeriodicalIF":0.7,"publicationDate":"2021-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80573180","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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