{"title":"Doubly Slice Montesinos Links","authors":"D. McCoy, Clayton McDonald","doi":"10.1307/mmj/20216077","DOIUrl":"https://doi.org/10.1307/mmj/20216077","url":null,"abstract":"This paper compares notions of double sliceness for links. The main result is to show that a large family of 2-component Montesinos links are not strongly doubly slice despite being weakly doubly slice and having doubly slice components. Our principal obstruction to strong double slicing comes by considering branched double covers. To this end we prove a result classifying Seifert fibered spaces which admit a smooth embeddings into integer homology $S^1 times S^3$s by maps inducing surjections on the first homology group. A number of other results and examples pertaining to doubly slice links are also given.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85738132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Clark Measures for Rational Inner Functions","authors":"K. Bickel, J. Cima, A. Sola","doi":"10.1307/mmj/20216046","DOIUrl":"https://doi.org/10.1307/mmj/20216046","url":null,"abstract":"We analyze the fine structure of Clark measures and Clark isometries associated with two-variable rational inner functions on the bidisk. In the degree (n, 1) case, we give a complete description of supports and weights for both generic and exceptional Clark measures, characterize when the associated embedding operators are unitary, and give a formula for those embedding operators. We also highlight connections between our results and both the structure of Agler decompositions and study of extreme points for the set of positive pluriharmonic measures on 2-torus.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79249120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hybrid Bounds on Two-Parametric Families of Weyl Sums Along Smooth Curves","authors":"Chang-Pao Chen, I. Shparlinski","doi":"10.1307/mmj/20205904","DOIUrl":"https://doi.org/10.1307/mmj/20205904","url":null,"abstract":"","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76850854","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Ga3-Structures on del Pezzo Fibrations","authors":"Masaru Nagaoka","doi":"10.1307/MMJ/20195835","DOIUrl":"https://doi.org/10.1307/MMJ/20195835","url":null,"abstract":"","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85898395","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Multiplicative p -Adic Approximation","authors":"D. Badziahin, Y. Bugeaud","doi":"10.1307/mmj/20195785","DOIUrl":"https://doi.org/10.1307/mmj/20195785","url":null,"abstract":"Let p be a prime number. We give several results towards a particular instance of a conjecture of Einsiedler and Kleinbock asserting that every p-adic number x satisfies inf a,b∈Z∖{0}|ab|⋅|ax−b|p=0. We highlight a close relationship between this conjecture and the (still open) p-adic Littlewood conjecture, according to which every real number ξ satisfies inf q∈Z,q⩾1q⋅‖qξ‖⋅|q|p=0. Furthermore, we discuss the analogues of these conjectures over fields of power series.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86613645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Self-Affine Property of Evolutional Type Appearing in a Hamilton–Jacobi Flow Starting from the Takagi Function","authors":"Y. Fujita, N. Hamamuki, Norikazu Yamaguchi","doi":"10.1307/mmj/20195782","DOIUrl":"https://doi.org/10.1307/mmj/20195782","url":null,"abstract":"In this paper, we study a Hamilton–Jacobi flow {Htτ}t>0 starting from the Takagi function τ. The Takagi function is well known as a pathological function that is everywhere continuous and nowhere differentiable on R. As the first result of this paper, we derive an explicit representation of {Htτ}. It turns out that Htτ is a piecewise quadratic function at any time and that the points of intersection between the parabolas are given in terms of binary expansion of real numbers. Applying the representation formula, we next give the main result, which asserts that {Htτ} has a self-affine property of evolutional type involving a time difference in the functional equality. Furthermore, we determine the optimal time until when the self-affine property is valid.","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91157733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the Fixed Point Method and Bloch’s Theorem","authors":"J. Cortissoz","doi":"10.1307/MMJ/20195829","DOIUrl":"https://doi.org/10.1307/MMJ/20195829","url":null,"abstract":"","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79550271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Lower Bound for the Hausdorff Dimension of the Green Current","authors":"H. Thelin","doi":"10.1307/MMJ/20195844","DOIUrl":"https://doi.org/10.1307/MMJ/20195844","url":null,"abstract":"","PeriodicalId":49820,"journal":{"name":"Michigan Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78039020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}