Proceedings of the American Mathematical Society, Series B最新文献

{"title":"Bounds for the Tornheim double zeta function","authors":"Takashi Nakamura","doi":"10.1090/bproc/142","DOIUrl":"https://doi.org/10.1090/bproc/142","url":null,"abstract":"<p>In the present paper, we give bounds for the Tornheim double zeta function <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T left-parenthesis s 1 comma s 2 comma s 3 right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>T</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>s</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>s</mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>s</mml:mi>\u0000 <mml:mn>3</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">T(s_1,s_2,s_3)</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> when <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartAbsoluteValue t 1 EndAbsoluteValue comma StartAbsoluteValue t 2 EndAbsoluteValue comma StartAbsoluteValue t 3 EndAbsoluteValue greater-than-or-equal-to 1\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">|<!-- | --></mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">|<!-- | --></mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">|<!-- | --></mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">|<!-- | --></mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">|<!-- | --></mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mn>3</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">|<!-- | --></mml:mo>\u0000 <mml:mo>≥<!-- ≥ --></mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">lvert t_1 rvert , lvert t_2 rvert , lvert t_3 rvert ge 1</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"StartAbsoluteValue t 1 plus t 2 EndAbsoluteValue comma StartAbsoluteValue t 2 plus t 3 EndAbsoluteValue comma StartAbsoluteValue t 3 plus t 1 EndAbsoluteValue greater-than-or-equal-to 1\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">|<!-- | --></mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo>+</mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">|<!-- | --></mml:mo>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mo fence=\"false\" stretchy=\"false\">|<!-- | --></mml:mo>\u0000 <mml:msub>\u0000 <mml:mi>t</mml:mi>\u0000 <mml:mn>2</mml:mn>\u0000 </mml:msub>\u0000 <mml:mo>+</mml:","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126336752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sarnak’s conjecture for a class of rank-one subshifts","authors":"Mahmood Etedadialiabadi, Su Gao","doi":"10.1090/bproc/148","DOIUrl":"https://doi.org/10.1090/bproc/148","url":null,"abstract":"Using techniques developed by Kanigowski, Lemańczyk, and Radziwiłł [Fund. Math. 255 (2021), pp. 309–336], we verify Sarnak’s conjecture for two classes of rank-one subshifts with unbounded cutting parameters. The first class of rank-one subshifts we consider is called almost complete congruency classes (accc), the definition of which is motivated by the main result of Foreman, Gao, Hill, Silva, and Weiss [Isr. J. Math., To appear], which implies that when a rank-one subshift carries a unique nonatomic invariant probability measure, it is accc if it is measure-theoretically isomorphic to an odometer. The second class we consider consists of Katok’s map and its generalizations.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128159794","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A 4-fold categorical equivalence","authors":"Ray Maresca","doi":"10.1090/bproc/178","DOIUrl":"https://doi.org/10.1090/bproc/178","url":null,"abstract":"In this note, we will illuminate some immediate consequences of work done by Reineke in [Algebr. Represent. Theory 16 (2013), no. 5. 1313–1314] that may prove to be useful in the study of elliptic curves. In particular, we will construct an isomorphism between the category of smooth projective curves with a category of quiver Grassmannians. We will use this to provide a 4-fold categorical equivalence between a category of quiver Grassmannians, smooth projective curves, compact Riemann surfaces, and fields of transcendence degree 1 over \u0000\u0000 \u0000 \u0000 C\u0000 \u0000 mathbb {C}\u0000 \u0000\u0000. We finish with noting that the category of elliptic curves is isomorphic to a category of quiver Grassmannians, whence providing an analytic group structure to a class of quiver Grassmannians.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129857600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A modular construction of unramified 𝑝-extensions of ℚ(ℕ^{1/𝕡})","authors":"Jaclyn Lang, Preston Wake","doi":"10.1090/bproc/141","DOIUrl":"https://doi.org/10.1090/bproc/141","url":null,"abstract":"<p>We show that for primes <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N comma p greater-than-or-equal-to 5\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:mo>,</mml:mo>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:mo>≥<!-- ≥ --></mml:mo>\u0000 <mml:mn>5</mml:mn>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">N, p geq 5</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> with <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N identical-to negative 1 mod p\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:mo>≡<!-- ≡ --></mml:mo>\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo lspace=\"thickmathspace\" rspace=\"thickmathspace\">mod</mml:mo>\u0000 <mml:mi>p</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">N equiv -1 bmod p</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, the class number of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper Q left-parenthesis upper N Superscript 1 slash p Baseline right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi mathvariant=\"double-struck\">Q</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msup>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo>/</mml:mo>\u0000 </mml:mrow>\u0000 <mml:mi>p</mml:mi>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">mathbb {Q}(N^{1/p})</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> is divisible by <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\">\u0000 <mml:semantics>\u0000 <mml:mi>p</mml:mi>\u0000 <mml:annotation encoding=\"application/x-tex\">p</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>. Our methods are via congruences between Eisenstein series and cusp forms. In particular, we show that when <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper N identical-to negative 1 mod p\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>N</mml:mi>\u0000 <mml:mo>≡<!-- ≡ --></mml:mo>\u0000 <mml:mo>−<!-- − --></mml:mo>\u0000 <mml:mn>1</mml:mn>\u0000 <mml:mo lspace=\"thickmathspace\" rspace=\"thickmathspace\">mod</mml:mo>\u0000 <mml:mi>p</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">N equiv -1 bmod p</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>, there is always a cusp form of weight <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"148 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114569092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Milnor operations and classifying spaces","authors":"Masaki Kameko","doi":"10.1090/bproc/177","DOIUrl":"https://doi.org/10.1090/bproc/177","url":null,"abstract":"We give an example of a nonzero odd degree element of the classifying space of a connected Lie group such that all higher Milnor operations vanish on it. It is a counterexample of a conjecture of Kono and Yagita [Trans. Amer. Math. Soc. 339 (1993), pp. 781–798].","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130469789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Alternative proofs of Mandrekar’s theorem","authors":"Linus Bergqvist","doi":"10.1090/bproc/156","DOIUrl":"https://doi.org/10.1090/bproc/156","url":null,"abstract":"We present two alternative proofs of Mandrekar’s theorem, which states that an invariant subspace of the Hardy space on the bidisc is of Beurling type precisely when the shifts satisfy a doubly commuting condition [Proc. Amer. Math. Soc. 103 (1988), pp. 145–148]. The first proof uses properties of Toeplitz operators to derive a formula for the reproducing kernel of certain shift invariant subspaces, which can then be used to characterize them. The second proof relies on the reproducing property in order to show that the reproducing kernel at the origin must generate the entire shift invariant subspace.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121963852","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Toeplitz separability, entanglement, and complete positivity using operator system duality","authors":"D. Farenick, Michelle McBurney","doi":"10.1090/bproc/163","DOIUrl":"https://doi.org/10.1090/bproc/163","url":null,"abstract":"<p>A new proof is presented of a theorem of L. Gurvits [LANL Unclassified Technical Report (2001), LAUR–01–2030], which states that the cone of positive block-Toeplitz matrices with matrix entries has no entangled elements. The proof of the Gurvits separation theorem is achieved by making use of the structure of the operator system dual of the operator system <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C left-parenthesis upper S Superscript 1 Baseline right-parenthesis Superscript left-parenthesis n right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>C</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msup>\u0000 <mml:mi>S</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msup>\u0000 <mml:msup>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">C(S^1)^{(n)}</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n times n\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo>×<!-- × --></mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 </mml:mrow>\u0000 <mml:annotation encoding=\"application/x-tex\">ntimes n</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula> Toeplitz matrices over the complex field, and by determining precisely the structure of the generators of the extremal rays of the positive cones of the operator systems <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper C left-parenthesis upper S Superscript 1 Baseline right-parenthesis Superscript left-parenthesis n right-parenthesis circled-times Subscript min Baseline script upper B left-parenthesis script upper H right-parenthesis\">\u0000 <mml:semantics>\u0000 <mml:mrow>\u0000 <mml:mi>C</mml:mi>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:msup>\u0000 <mml:mi>S</mml:mi>\u0000 <mml:mn>1</mml:mn>\u0000 </mml:msup>\u0000 <mml:msup>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mi>n</mml:mi>\u0000 <mml:mo stretchy=\"false\">)</mml:mo>\u0000 </mml:mrow>\u0000 </mml:msup>\u0000 <mml:msub>\u0000 <mml:mo>⊗<!-- ⊗ --></mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mtext>min</mml:mtext>\u0000 </mml:mrow>\u0000 </mml:msub>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">B</mml:mi>\u0000 </mml:mrow>\u0000 <mml:mo stretchy=\"false\">(</mml:mo>\u0000 <mml:mrow class=\"MJX-TeXAtom-ORD\">\u0000 <mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">H</mml:mi>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123999773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Kac formula and Poincaré recurrence theorem in Riesz spaces","authors":"Youssef Azouzi, M. B. Amor, Jonathan Homann, Marwa Masmoudi, B. Watson","doi":"10.1090/bproc/152","DOIUrl":"https://doi.org/10.1090/bproc/152","url":null,"abstract":"Riesz space (non-pointwise) generalizations for iterative processes are given for the concepts of recurrence, first recurrence and conditional ergodicity. Riesz space conditional versions of the Poincaré Recurrence Theorem and the Kac formula are developed. Under mild assumptions, it is shown that every conditional expectation preserving process is conditionally ergodic with respect to the conditional expectation generated by the Cesàro mean associated with the iterates of the process. Applied to processes in \u0000\u0000 \u0000 \u0000 \u0000 L\u0000 1\u0000 \u0000 (\u0000 Ω\u0000 ,\u0000 \u0000 \u0000 A\u0000 \u0000 \u0000 ,\u0000 μ\u0000 )\u0000 \u0000 L^1(Omega ,{mathcal A},mu )\u0000 \u0000\u0000, where \u0000\u0000 \u0000 μ\u0000 mu\u0000 \u0000\u0000 is a probability measure, new conditional versions of the above theorems are obtained.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131317231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Tower equivalence and Lusztig’s truncated Fourier transform","authors":"J. Michel","doi":"10.1090/bproc/167","DOIUrl":"https://doi.org/10.1090/bproc/167","url":null,"abstract":"If \u0000\u0000 \u0000 f\u0000 f\u0000 \u0000\u0000 denotes the truncated Lusztig Fourier transform, we show that the image by \u0000\u0000 \u0000 f\u0000 f\u0000 \u0000\u0000 of the normalized characteristic function of a Coxeter element is the alternate sum of the exterior powers of the reflection representation, and that any class function is tower equivalent to its image by \u0000\u0000 \u0000 f\u0000 f\u0000 \u0000\u0000. In particular this gives a proof of the results of Chapuy and Douvropoulos on “Coxeter factorizations with generalized Jucys-Murphy weights and matrix tree theorems for reflection groups” for irreducible spetsial reflection groups, based on Deligne-Lusztig combinatorics.","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126714163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Remarks on the Navier-Stokes equations in space dimension 𝑛≥3","authors":"Jishan Fan, T. Ozawa","doi":"10.1090/bproc/135","DOIUrl":"https://doi.org/10.1090/bproc/135","url":null,"abstract":"<p>In this paper, we prove some new <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript p\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mi>p</mml:mi>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">L^p</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-estimates of the velocity by the technique of <inline-formula content-type=\"math/mathml\">\u0000<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript p\">\u0000 <mml:semantics>\u0000 <mml:msup>\u0000 <mml:mi>L</mml:mi>\u0000 <mml:mi>p</mml:mi>\u0000 </mml:msup>\u0000 <mml:annotation encoding=\"application/x-tex\">L^p</mml:annotation>\u0000 </mml:semantics>\u0000</mml:math>\u0000</inline-formula>-energy method.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116990400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}