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A generalization of Weingartner’s theorem related to the Riemann hypothesis 关于黎曼假设的Weingartner定理的推广
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-05-19 DOI: 10.1007/s00013-026-02256-9
Jongho Yang
{"title":"A generalization of Weingartner’s theorem related to the Riemann hypothesis","authors":"Jongho Yang","doi":"10.1007/s00013-026-02256-9","DOIUrl":"10.1007/s00013-026-02256-9","url":null,"abstract":"<div><p>In the study of the Riemann hypothesis, Báez-Duarte provided a strong version of the Nyman–Beurling criterion by considering the approximation of the characteristic function using natural Beurling functions in <span>(L^2)</span>. Later, Balazard and Saias posed a question regarding the coefficients of these natural Beurling functions, which Weingartner answered using the sequence space <span>(l^2)</span>. In this paper, we extend Weingartner’s theorem to the Banach space <span>(L^p)</span>, a setting that is more difficult to handle than the Hilbert space <span>(l^2)</span>. We also show that the Beurling functions form the unique best minimal system for approximating the characteristic function in <span>(L^p)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 6","pages":"625 - 633"},"PeriodicalIF":0.6,"publicationDate":"2026-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285472","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}
引用次数: 0
Correction to: Hypercyclic composition operators on the (S^p) space with automorphism symbols 修正：(S^p)空间上带有自同构符号的超循环复合算子
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-05-14 DOI: 10.1007/s00013-026-02248-9
Cao Jiang, Shi-An Han, Ze-Hua Zhou
{"title":"Correction to: Hypercyclic composition operators on the (S^p) space with automorphism symbols","authors":"Cao Jiang,&nbsp;Shi-An Han,&nbsp;Ze-Hua Zhou","doi":"10.1007/s00013-026-02248-9","DOIUrl":"10.1007/s00013-026-02248-9","url":null,"abstract":"","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 6","pages":"649 - 651"},"PeriodicalIF":0.6,"publicationDate":"2026-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285474","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}
引用次数: 0
A generalization of Dumas’ irreducibility criterion 杜马不可约准则的推广
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-05-12 DOI: 10.1007/s00013-026-02249-8
Jitender Singh
{"title":"A generalization of Dumas’ irreducibility criterion","authors":"Jitender Singh","doi":"10.1007/s00013-026-02249-8","DOIUrl":"10.1007/s00013-026-02249-8","url":null,"abstract":"<div><p>Using Newton polygons, a key factorization result for polynomials over discrete valuation domains is proved, which in particular yields new irreducibility criteria including a generalization of the classical irreducibility criterion of Dumas.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 6","pages":"571 - 581"},"PeriodicalIF":0.6,"publicationDate":"2026-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285467","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}
引用次数: 0
Monomial curves and locally linear resolution 单项式曲线和局部线性分辨率
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-05-12 DOI: 10.1007/s00013-026-02235-0
Takayuki Hibi, Peter Schenzel
{"title":"Monomial curves and locally linear resolution","authors":"Takayuki Hibi,&nbsp;Peter Schenzel","doi":"10.1007/s00013-026-02235-0","DOIUrl":"10.1007/s00013-026-02235-0","url":null,"abstract":"<div><p>For four elements of a Noetherian ring, we construct complexes of free modules of length three (resp. five) by an explicit description of the homomorphisms of the free modules. We provide exactness criteria for them. As an application, we use these results in order to describe explicitly the minimal free resolution of the Hartshorne–Rao module of a monomial curve lying on a smooth quadric. Also it provides an example of linearly generated module with syzygies of arbitrary high degree.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 5","pages":"471 - 481"},"PeriodicalIF":0.5,"publicationDate":"2026-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147968103","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}
引用次数: 0
On the stability of the periodic traveling waves of the quadratic-cubic Boussinesq equation 二次-三次Boussinesq方程周期行波的稳定性
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-05-06 DOI: 10.1007/s00013-026-02230-5
Sevdzhan Hakkaev
{"title":"On the stability of the periodic traveling waves of the quadratic-cubic Boussinesq equation","authors":"Sevdzhan Hakkaev","doi":"10.1007/s00013-026-02230-5","DOIUrl":"10.1007/s00013-026-02230-5","url":null,"abstract":"<div><p>The question of the spectral stability of periodic waves of cnoidal and snoidal types for the Boussinesq equation is considered. The main results are that, for some values of the parameters, the periodic cnoidal waves are spectrally stable and unstable for others, with respect to perturbations of the same period. For the snoidal waves, we have that they are stable for all values of the parameters. Our approach, which turns out to give a definite answer for the entire domain of parameters, relies on the instability index theory, as developed by Lin and Zeng (Mem Am Math Soc 275(1347):136, 2022).</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 5","pages":"527 - 540"},"PeriodicalIF":0.5,"publicationDate":"2026-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147968110","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}
引用次数: 0
Postulation number of symbolic powers of certain two-dimensional monomial ideals 某些二维单项式理想的符号幂的假设数
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-04-27 DOI: 10.1007/s00013-026-02245-y
Nguyên Quang Lôc, Nguyên Công Minh, Phan Thi Thuy
{"title":"Postulation number of symbolic powers of certain two-dimensional monomial ideals","authors":"Nguyên Quang Lôc,&nbsp;Nguyên Công Minh,&nbsp;Phan Thi Thuy","doi":"10.1007/s00013-026-02245-y","DOIUrl":"10.1007/s00013-026-02245-y","url":null,"abstract":"<div><p>In this paper, we investigate the linear behavior of the postulation number of the symbolic powers of certain two-dimensional monomial ideals.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 6","pages":"583 - 595"},"PeriodicalIF":0.6,"publicationDate":"2026-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285471","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}
引用次数: 0
On the decimal and octal digits of 1/p 1/p的十进制和八进制数字
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-04-24 DOI: 10.1007/s00013-026-02252-z
Kurt Girstmair
{"title":"On the decimal and octal digits of 1/p","authors":"Kurt Girstmair","doi":"10.1007/s00013-026-02252-z","DOIUrl":"10.1007/s00013-026-02252-z","url":null,"abstract":"<div><p>Let <i>p</i> be a prime <span>(equiv 3)</span> mod 4, <span>(p&gt;3)</span>, and suppose that 10 has the order <span>((p-1)/2)</span> mod <i>p</i>. Then 1/<i>p</i> has a decimal period of length <span>((p-1)/2)</span>. We express the frequency of each digit <span>(0,ldots ,9)</span> in this period in terms of the class numbers of two imaginary quadratic number fields. We also exhibit certain analogues of this result, so for the case that 10 is a primitive root mod <i>p</i> and for the octal digits of 1/<i>p</i>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 6","pages":"615 - 623"},"PeriodicalIF":0.6,"publicationDate":"2026-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285468","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}
引用次数: 0
Artin–Schreier–Witt extensions and ramification breaks Artin-Schreier-Witt延伸和分支断裂
IF 0.5 4区 数学
Archiv der Mathematik Pub Date : 2026-04-24 DOI: 10.1007/s00013-026-02234-1
G. Griffith Elder, Kevin Keating
{"title":"Artin–Schreier–Witt extensions and ramification breaks","authors":"G. Griffith Elder,&nbsp;Kevin Keating","doi":"10.1007/s00013-026-02234-1","DOIUrl":"10.1007/s00013-026-02234-1","url":null,"abstract":"<div><p>Let <span>(K=k((t)))</span> be a local field of characteristic <span>(p&gt;0)</span> with perfect residue field <i>k</i>. Let <span>(vec {a}=(a_0,a_1,dots ,a_{n-1})in W_n(K))</span> be a Witt vector of length <i>n</i>. Assume that <span>(vec {a})</span> is “reduced”, and that <span>(v_K(a_0)&lt;0)</span>; then Artin–Schreier–Witt theory associates to <span>(vec {a})</span> a totally ramified cyclic extension <i>L</i>/<i>K</i> of degree <span>(p^n)</span>. In the case where <i>k</i> is finite, several authors have used class field theory to explicitly compute the upper ramification breaks of <i>L</i>/<i>K</i> in terms of the valuations of the components of <span>(vec {a})</span>. In this note, we use a direct method to show that these formulas remain valid when <i>k</i> is an arbitrary perfect field.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 5","pages":"461 - 469"},"PeriodicalIF":0.5,"publicationDate":"2026-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147968199","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}
引用次数: 0
A note on complete evolution algebras 关于完全演化代数的注解
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-04-22 DOI: 10.1007/s00013-026-02251-0
Xabier García-Martínez, Andrés Pérez-Rodríguez
{"title":"A note on complete evolution algebras","authors":"Xabier García-Martínez,&nbsp;Andrés Pérez-Rodríguez","doi":"10.1007/s00013-026-02251-0","DOIUrl":"10.1007/s00013-026-02251-0","url":null,"abstract":"<div><p>This short note provides positive answers to two conjectures of Camacho, Khudoyberdiyev, and Omirov on the classification of complete evolution algebras. Our approach is based on analysing the solution set of a generic non-linear polynomial system of equations using elementary tools from algebraic geometry. We also obtain new results on subalgebras and idempotents of evolution algebras, and conclude by proposing a conjecture that may characterise solvable evolution algebras.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 6","pages":"597 - 604"},"PeriodicalIF":0.6,"publicationDate":"2026-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-026-02251-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285473","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}
引用次数: 0
On transitive sets of derangements in primitive groups 关于原始群中无序的传递集
IF 0.6 4区 数学
Archiv der Mathematik Pub Date : 2026-04-20 DOI: 10.1007/s00013-026-02240-3
Peter Müller
{"title":"On transitive sets of derangements in primitive groups","authors":"Peter Müller","doi":"10.1007/s00013-026-02240-3","DOIUrl":"10.1007/s00013-026-02240-3","url":null,"abstract":"<div><p>We construct a primitive permutation action of the Steinberg triality group <img> of degree 4, 064, 256 and show that there are distinct points <span>(alpha ,beta )</span> such that there is no derangement <img> with <span>(alpha ^g=beta )</span>. This answers a question by John G. Thompson (Problem 8.75 in the Kourovka Notebook) in the negative.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":"126 6","pages":"551 - 556"},"PeriodicalIF":0.6,"publicationDate":"2026-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00013-026-02240-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148285469","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}
引用次数: 0
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