Bulletin of the Australian Mathematical Society最新文献

{"title":"A NOTE ON THE ZEROS OF L-FUNCTIONS ASSOCIATED TO FIXED-ORDER DIRICHLET CHARACTERS","authors":"C. C. CORRIGAN","doi":"10.1017/s0004972723001156","DOIUrl":"https://doi.org/10.1017/s0004972723001156","url":null,"abstract":"<p>We use the Weyl bound for Dirichlet <span>L</span>-functions to derive zero-density estimates for <span>L</span>-functions associated to families of fixed-order Dirichlet characters. The results improve on previous bounds given by the author when <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231216081215188-0622:S0004972723001156:S0004972723001156_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$sigma $</span></span></img></span></span> is sufficiently distant from the critical line.</p>","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"36 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138715123","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":"ANY DUAL OPERATOR SPACE IS WEAKLY LOCALLY REFLEXIVE","authors":"ZHE DONG, JINZE JIANG, YAFEI ZHAO","doi":"10.1017/s0004972723001120","DOIUrl":"https://doi.org/10.1017/s0004972723001120","url":null,"abstract":"<p>We introduce the notion of weakly local reflexivity in operator space theory and prove that any dual operator space is weakly locally reflexive.</p>","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"10 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138575739","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":"Stochastic Matching Models","authors":"Behrooz Niknami","doi":"10.1017/s0004972723001144","DOIUrl":"https://doi.org/10.1017/s0004972723001144","url":null,"abstract":"","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"48 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139009806","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":"NEW EFFECTIVE RESULTS IN THE THEORY OF THE RIEMANN ZETA-FUNCTION","authors":"A. Simonič","doi":"10.1017/s0004972723001132","DOIUrl":"https://doi.org/10.1017/s0004972723001132","url":null,"abstract":"","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"19 25","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138977190","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":"ADDITIVE COMPLETION OF THIN SETS","authors":"JIN-HUI FANG, CSABA SÁNDOR","doi":"10.1017/s0004972723001016","DOIUrl":"https://doi.org/10.1017/s0004972723001016","url":null,"abstract":"Two sets &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline1.png\" /&gt; &lt;jats:tex-math&gt; $A,B$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; of positive integers are called &lt;jats:italic&gt;exact additive complements&lt;/jats:italic&gt; if &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline2.png\" /&gt; &lt;jats:tex-math&gt; $A+B$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; contains all sufficiently large integers and &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline3.png\" /&gt; &lt;jats:tex-math&gt; $A(x)B(x)/xrightarrow 1$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;. For &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline4.png\" /&gt; &lt;jats:tex-math&gt; $A={a_1&lt;a_2&lt;cdots }$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, let &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline5.png\" /&gt; &lt;jats:tex-math&gt; $A(x)$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; denote the counting function of &lt;jats:italic&gt;A&lt;/jats:italic&gt; and let &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline6.png\" /&gt; &lt;jats:tex-math&gt; $a^*(x)$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; denote the largest element in &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline7.png\" /&gt; &lt;jats:tex-math&gt; $Abigcap [1,x]$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;. Following the work of Ruzsa [‘Exact additive complements’, &lt;jats:italic&gt;Quart. J. Math.&lt;/jats:italic&gt;68 (2017) 227–235] and Chen and Fang [‘Additive complements with Narkiewicz’s condition’, &lt;jats:italic&gt;Combinatorica&lt;/jats:italic&gt;39 (2019), 813–823], we prove that, for exact additive complements &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline8.png\" /&gt; &lt;jats:tex-math&gt; $A,B$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; with &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0004972723001016_inline9.png\" /&gt; &lt;jats:tex-math&gt; ${a_{n+1}}/ {na_n}rightarrow infty $ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, &lt;jats:disp-formula&gt; &lt;jats:alternatives&gt; &lt;jats:graphic xmlns:xlink=\"http:","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"220 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138495304","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":"AUTHOR INDEX FOR VOLUME 108","authors":"","doi":"10.1017/s0004972722001538","DOIUrl":"https://doi.org/10.1017/s0004972722001538","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"31 S105","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343221","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":"BAZ volume 108 issue 3 Cover and Back matter","authors":"","doi":"10.1017/s0004972722001526","DOIUrl":"https://doi.org/10.1017/s0004972722001526","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"30 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135343235","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 ENDOMORPHISMS OF EXTENSIONS IN TANNAKIAN CATEGORIES","authors":"PAYMAN ESKANDARI","doi":"10.1017/s0004972723001090","DOIUrl":"https://doi.org/10.1017/s0004972723001090","url":null,"abstract":"Abstract We prove analogues of Schur’s lemma for endomorphisms of extensions in Tannakian categories. More precisely, let $mathbf {T}$ be a neutral Tannakian category over a field of characteristic zero. Let E be an extension of A by B in $mathbf {T}$ . We consider conditions under which every endomorphism of E that stabilises B induces a scalar map on $Aoplus B$ . We give a result in this direction in the general setting of arbitrary $mathbf {T}$ and E , and then a stronger result when $mathbf {T}$ is filtered and the associated graded objects to A and B satisfy some conditions. We also discuss the sharpness of the results.","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"12 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135480126","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 EFFECTIVE BOUND FOR GENERALISED DIOPHANTINE <i>m</i>-TUPLES","authors":"SAUNAK BHATTACHARJEE, ANUP B. DIXIT, DISHANT SAIKIA","doi":"10.1017/s0004972723001077","DOIUrl":"https://doi.org/10.1017/s0004972723001077","url":null,"abstract":"Abstract For $kgeq 2$ and a nonzero integer n , a generalised Diophantine m -tuple with property $D_k(n)$ is a set of m positive integers $S = {a_1,a_2,ldots , a_m}$ such that $a_ia_j + n$ is a k th power for $1leq i< jleq m$ . Define $M_k(n):= text {sup}{|S| : S$ having property $D_k(n)}$ . Dixit et al . [‘Generalised Diophantine m -tuples’, Proc. Amer. Math. Soc. 150 (4) (2022), 1455–1465] proved that $M_k(n)=O(log n)$ , for a fixed k , as n varies. In this paper, we obtain effective upper bounds on $M_k(n)$ . In particular, we show that for $kgeq 2$ , $M_k(n) leq 3,phi (k) log n$ if n is sufficiently large compared to k .","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135634080","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 DIFFERENCE ANALOGUE OF THE TUMURA–HAYMAN–CLUNIE THEOREM","authors":"MINGLIANG FANG, HUI LI, XIAO YAO","doi":"10.1017/s0004972723001089","DOIUrl":"https://doi.org/10.1017/s0004972723001089","url":null,"abstract":"Abstract We prove a difference analogue of the celebrated Tumura–Hayman–Clunie theorem. Let f be a transcendental entire function, let c be a nonzero constant and let n be a positive integer. If f and $Delta _c^n f$ omit zero in the whole complex plane, then either $f(z)=exp (h_1(z)+C_1 z)$ , where $h_1$ is an entire function of period c and $exp (C_1 c)neq 1$ , or $f(z)=exp (h_2(z)+C_2 z)$ , where $h_2$ is an entire function of period $2c$ and $C_2$ satisfies $$ begin{align*} bigg(frac{1+exp(C_2c)}{1-exp(C_2 c)}bigg)^{2n}=1. end{align*} $$","PeriodicalId":50720,"journal":{"name":"Bulletin of the Australian Mathematical Society","volume":"90 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135634229","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}