{"title":"A steady stratified purely azimuthal flow representing the Antarctic Circumpolar Current.","authors":"Calin Iulian Martin, Ronald Quirchmayr","doi":"10.1007/s00605-019-01332-3","DOIUrl":"10.1007/s00605-019-01332-3","url":null,"abstract":"<p><p>We construct an explicit steady stratified purely azimuthal flow for the governing equations of geophysical fluid dynamics. These equations are considered in a setting that applies to the Antarctic Circumpolar Current, accounting for eddy viscosity and forcing terms.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"192 2","pages":"401-407"},"PeriodicalIF":0.9,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7220887/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37947749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An Essay on the foundations of geometry","authors":"Bertrand Russell Earl","doi":"10.1007/BF01696331","DOIUrl":"https://doi.org/10.1007/BF01696331","url":null,"abstract":"","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"1 1","pages":"A33-A34"},"PeriodicalIF":0.9,"publicationDate":"2018-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76675487","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":"Rationality for isobaric automorphic representations: the CM-case.","authors":"Harald Grobner","doi":"10.1007/s00605-018-1188-5","DOIUrl":"10.1007/s00605-018-1188-5","url":null,"abstract":"<p><p>In this note we prove a simultaneous extension of the author's joint result with M. Harris for critical values of Rankin-Selberg <i>L</i>-functions <math><mrow><mi>L</mi> <mo>(</mo> <mi>s</mi> <mo>,</mo> <mi>Π</mi> <mo>×</mo> <msup><mi>Π</mi> <mo>'</mo></msup> <mo>)</mo></mrow> </math> (Grobner and Harris in J Inst Math Jussieu 15:711-769, 2016, Thm. 3.9) to (i) general CM-fields <i>F</i> and (ii) cohomological automorphic representations <math> <mrow><msup><mi>Π</mi> <mo>'</mo></msup> <mo>=</mo> <msub><mi>Π</mi> <mn>1</mn></msub> <mo>⊞</mo> <mo>⋯</mo> <mo>⊞</mo> <msub><mi>Π</mi> <mi>k</mi></msub> </mrow> </math> which are the isobaric sum of unitary cuspidal automorphic representations <math><msub><mi>Π</mi> <mi>i</mi></msub> </math> of general linear groups of arbitrary rank over <i>F</i>. In this sense, the main result of these notes, cf. Theorem 1.9, is a generalization, as well as a complement, of the main results in Raghuram (Forum Math 28:457-489, 2016; Int Math Res Not 2:334-372, 2010. https://doi.org/10.1093/imrn/rnp127), and Mahnkopf (J Inst Math Jussieu 4:553-637, 2005).</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"187 1","pages":"79-94"},"PeriodicalIF":0.9,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6428343/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37127955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Matrix Riemann-Hilbert problems with jumps across Carleson contours.","authors":"Jonatan Lenells","doi":"10.1007/s00605-017-1019-0","DOIUrl":"https://doi.org/10.1007/s00605-017-1019-0","url":null,"abstract":"<p><p>We develop a theory of <math><mrow><mi>n</mi> <mo>×</mo> <mi>n</mi></mrow> </math> -matrix Riemann-Hilbert problems for a class of jump contours and jump matrices of low regularity. Our basic assumption is that the contour <math><mi>Γ</mi></math> is a finite union of simple closed Carleson curves in the Riemann sphere. In particular, unbounded contours with cusps, corners, and nontransversal intersections are allowed. We introduce a notion of <math><msup><mi>L</mi> <mi>p</mi></msup> </math> -Riemann-Hilbert problem and establish basic uniqueness results and Fredholm properties. We also investigate the implications of Fredholmness for the unique solvability and prove a theorem on contour deformation.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"186 1","pages":"111-152"},"PeriodicalIF":0.9,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00605-017-1019-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37377945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Explicit upper bound for the average number of divisors of irreducible quadratic polynomials.","authors":"Kostadinka Lapkova","doi":"10.1007/s00605-017-1061-y","DOIUrl":"https://doi.org/10.1007/s00605-017-1061-y","url":null,"abstract":"<p><p>Consider the divisor sum <math><mrow><msub><mo>∑</mo><mrow><mi>n</mi><mo>≤</mo><mi>N</mi></mrow></msub><mi>τ</mi><mrow><mo>(</mo><msup><mi>n</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>b</mi><mi>n</mi><mo>+</mo><mi>c</mi><mo>)</mo></mrow></mrow></math> for integers <i>b</i> and <i>c</i>. We extract an asymptotic formula for the average divisor sum in a convenient form, and provide an explicit upper bound for this sum with the correct main term. As an application we give an improvement of the maximal possible number of <math><mrow><mi>D</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow></math> -quadruples.</p>","PeriodicalId":54737,"journal":{"name":"Monatshefte fur Mathematik","volume":"186 4","pages":"663-673"},"PeriodicalIF":0.9,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00605-017-1061-y","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36389688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}