Forum Mathematicum最新文献

Discrete Ω-results for the Riemann zeta function 黎曼zeta函数的离散Ω结果

IF 0.8 3区数学

Forum Mathematicum Pub Date : 2024-09-02 DOI: 10.1515/forum-2023-0324

Paolo Minelli, Athanasios Sourmelidis

{"title":"Discrete Ω-results for the Riemann zeta function","authors":"Paolo Minelli, Athanasios Sourmelidis","doi":"10.1515/forum-2023-0324","DOIUrl":"https://doi.org/10.1515/forum-2023-0324","url":null,"abstract":"We study lower bounds for the Riemann zeta function <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>ζ</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>s</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> {zeta(s)} along vertical arithmetic progressions in the right-half of the critical strip. We show that the lower bounds obtained in the discrete case coincide, up to the constants in the exponential, with the ones known for the continuous case, that is when the imaginary part of s ranges on a given interval. Our methods are based on a discretization of the resonance method for estimating extremal values of <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>ζ</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>s</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> {zeta(s)} .","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"24 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202185","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}

引用次数: 0

The stable category of monomorphisms between (Gorenstein) projective modules with applications (戈伦斯坦)射影模块间单态的稳定范畴及其应用

IF 0.8 3区数学

Forum Mathematicum Pub Date : 2024-09-02 DOI: 10.1515/forum-2023-0317

Abdolnaser Bahlekeh, Fahimeh Sadat Fotouhi, Mohammad Amin Hamlehdari, Shokrollah Salarian

引用次数: 0

Is addition definable from multiplication and successor? 乘法和后继加法可以定义吗？

IF 0.8 3区数学

Forum Mathematicum Pub Date : 2024-09-02 DOI: 10.1515/forum-2024-0245

Friedrich Wehrung

引用次数: 0

Big pure projective modules over commutative noetherian rings: Comparison with the completion 交换诺特环上的大纯投影模块：与完形比较

IF 0.8 3区数学

Forum Mathematicum Pub Date : 2024-09-02 DOI: 10.1515/forum-2024-0031

Dolors Herbera, Pavel Příhoda, Roger Wiegand

{"title":"Big pure projective modules over commutative noetherian rings: Comparison with the completion","authors":"Dolors Herbera, Pavel Příhoda, Roger Wiegand","doi":"10.1515/forum-2024-0031","DOIUrl":"https://doi.org/10.1515/forum-2024-0031","url":null,"abstract":"A module over a ring <jats:italic>R</jats:italic> is <jats:italic>pure projective</jats:italic> provided it is isomorphic to a direct summand of a direct sum of finitely presented modules. We develop tools for the classification of pure projective modules over commutative noetherian rings. In particular, for a fixed finitely presented module <jats:italic>M</jats:italic>, we consider <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>Add</m:mi> <m:mo>⁡</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>M</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2024-0031_eq_1297.png\"/> <jats:tex-math>{operatorname{Add}(M)}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, which consists of direct summands of direct sums of copies of <jats:italic>M</jats:italic>. We are primarily interested in the case where <jats:italic>R</jats:italic> is a one-dimensional, local domain, and in torsion-free (or Cohen–Macaulay) modules. We show that, even in this case, <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>Add</m:mi> <m:mo>⁡</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>M</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2024-0031_eq_1297.png\"/> <jats:tex-math>{operatorname{Add}(M)}</jats:tex-math> </jats:alternatives> </jats:inline-formula> can have an abundance of modules that are not direct sums of finitely generated ones. Our work is based on the fact that such infinitely generated direct summands are all determined by finitely generated data. Namely, idempotent/trace ideals of the endomorphism ring of <jats:italic>M</jats:italic> and finitely generated projective modules modulo such idempotent ideals. This allows us to extend the classical theory developed to study the behaviour of direct sum decomposition of finitely generated modules comparing with their completion to the infinitely generated case. We study the structure of the monoid <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:msup> <m:mi>V</m:mi> <m:mo>*</m:mo> </m:msup> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>M</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_forum-2024-0031_eq_0807.png\"/> <jats:tex-math>{V^{*}(M)}</jats:tex-math> </jats:alternatives> </jats:inline-formula>, of isomorphism classes of countably generated modules in <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>Add</m:mi> <m:mo>⁡</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>M</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"6 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202181","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}

引用次数: 0

Any Sasakian structure is approximated by embeddings into spheres 任何萨萨基结构都可以通过嵌入球面来近似

IF 0.8 3区数学

Forum Mathematicum Pub Date : 2024-08-07 DOI: 10.1515/forum-2023-0364

Andrea Loi, Giovanni Placini

{"title":"Any Sasakian structure is approximated by embeddings into spheres","authors":"Andrea Loi, Giovanni Placini","doi":"10.1515/forum-2023-0364","DOIUrl":"https://doi.org/10.1515/forum-2023-0364","url":null,"abstract":"We show that, for any given <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>q</m:mi> <m:mo>≥</m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> {qgeq 0} , any Sasakian structure on a closed manifold M is approximated in the <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>C</m:mi> <m:mi>q</m:mi> </m:msup> </m:math> {C^{{q}}} -norm by structures induced by CR embeddings into weighted Sasakian spheres. In order to obtain this result, we also strengthen the approximation of an orbifold Kähler form by projectively induced ones given in [J. Ross and R. Thomas, Weighted projective embeddings, stability of orbifolds, and constant scalar curvature Kähler metrics, J. Differential Geom. 88 2011, 1, 109–159] in the <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>C</m:mi> <m:mn>0</m:mn> </m:msup> </m:math> {C^{0}} -norm to a <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:msup> <m:mi>C</m:mi> <m:mi>q</m:mi> </m:msup> </m:math> {C^{{q}}} -approximation.","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"161 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934834","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}

引用次数: 0

Quasi-triangular, factorizable Leibniz bialgebras and relative Rota–Baxter operators 准三角形、可因化莱布尼兹双桥和相对罗塔-巴克斯特算子

IF 0.8 3区数学

Forum Mathematicum Pub Date : 2024-08-05 DOI: 10.1515/forum-2023-0268

Chengming Bai, Guilai Liu, Yunhe Sheng, Rong Tang

引用次数: 0

Quantitative weighted estimates for the multilinear pseudo-differential operators in function spaces 函数空间多线性伪微分算子的定量加权估计

IF 0.8 3区数学

Forum Mathematicum Pub Date : 2024-08-05 DOI: 10.1515/forum-2023-0454

Jiawei Tan, Qingying Xue

引用次数: 0

A note on conjugacy of supplements in soluble periodic linear groups 关于可溶性周期线性群中的共轭补充物的说明

IF 0.8 3区数学

Forum Mathematicum Pub Date : 2024-08-04 DOI: 10.1515/forum-2024-0102

Marco Trombetti

{"title":"A note on conjugacy of supplements in soluble periodic linear groups","authors":"Marco Trombetti","doi":"10.1515/forum-2024-0102","DOIUrl":"https://doi.org/10.1515/forum-2024-0102","url":null,"abstract":"The aim of this short note is to prove that if G is a (homomorphic images of a) soluble periodic linear group and N is a locally nilpotent normal subgroup of G such that N and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>G</m:mi> <m:mo>/</m:mo> <m:mi>N</m:mi> </m:mrow> </m:math> {G/N} have no isomorphic G-chief factors, then two supplements to N in G are conjugate provided that they have the same intersection with N. This result follows from well-known theorems in the theory of Schunck classes (see [A. Ballester-Bolinches and L. M. Ezquerro, On conjugacy of supplements of normal subgroups of finite groups, Bull. Aust. Math. Soc. 89 2014, 2, 293–299]), and it appeared as the main theorem of [C. Parker and P. Rowley, A note on conjugacy of supplements in finite soluble groups, Bull. Lond. Math. Soc. 42 2010, 3, 417–419].","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"199 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934931","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}

引用次数: 0

Gradings and graded linear maps on algebras 代数上的分级和分级线性映射

IF 0.8 3区数学

Forum Mathematicum Pub Date : 2024-08-04 DOI: 10.1515/forum-2024-0098

Antonio Ioppolo, Fabrizio Martino

{"title":"Gradings and graded linear maps on algebras","authors":"Antonio Ioppolo, Fabrizio Martino","doi":"10.1515/forum-2024-0098","DOIUrl":"https://doi.org/10.1515/forum-2024-0098","url":null,"abstract":"Let A be a superalgebra over a field F of characteristic zero. We prove tight relations between graded automorphisms, pseudoautomorphisms, superautomorphisms and K-gradings on A, where K is the Klein group. Moreover, we investigate the consequences of such connections within the theory of polynomial identities. In the second part we focus on the superalgebra <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>U</m:mi> <m:mo>⁢</m:mo> <m:msub> <m:mi>T</m:mi> <m:mi>n</m:mi> </m:msub> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>F</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> {UT_{n}(F)} of <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>n</m:mi> <m:mo>×</m:mo> <m:mi>n</m:mi> </m:mrow> </m:math> {ntimes n} upper triangular matrices by completely classifying the graded-pseudo-super automorphism that one can define on it. Finally, we compute the ideals of identities of <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>U</m:mi> <m:mo>⁢</m:mo> <m:msub> <m:mi>T</m:mi> <m:mi>n</m:mi> </m:msub> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:mi>F</m:mi> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> {UT_{n}(F)} endowed with a graded or a pseudo automorphism, for any n, and the ideals of identities with superautomorphism in the cases <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>n</m:mi> <m:mo>=</m:mo> <m:mn>2</m:mn> </m:mrow> </m:math> {n=2} and <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>n</m:mi> <m:mo>=</m:mo> <m:mn>3</m:mn> </m:mrow> </m:math> {n=3} .","PeriodicalId":12433,"journal":{"name":"Forum Mathematicum","volume":"40 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141934929","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}

引用次数: 0

GIT quotient of holomorphic foliations on ℂℙ2 of degree 2 and quartic plane curves 度数为 2 的ℂℙ2 上全形叶形的 GIT 商和四元平面曲线

IF 0.8 3区数学

Forum Mathematicum Pub Date : 2024-08-04 DOI: 10.1515/forum-2024-0043

Claudia R. Alcántara, Juan Vásquez Aquino

引用次数: 0