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Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg最新文献

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Uniform bounds for the density in Artin’s conjecture for quadratic number fields 二次数场的Artin猜想中密度的统一界
IF 0.2 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2026-08-25 DOI: 10.1007/s12188-026-00300-7
Chi Wa Chan
{"title":"Uniform bounds for the density in Artin’s conjecture for quadratic number fields","authors":"Chi Wa Chan","doi":"10.1007/s12188-026-00300-7","DOIUrl":"10.1007/s12188-026-00300-7","url":null,"abstract":"<div><p>Let <i>K</i> be a quadratic number field and let <span>(alpha in K^times )</span> be not a root of unity. Under GRH there is a density <span>(textrm{dens}(alpha ))</span> of primes <span>(mathfrak {p})</span> of <i>K</i> such that <span>(alpha )</span> is a primitive root modulo <span>(mathfrak {p})</span>. We determine optimal lower and upper bounds for the ratio <span>(textrm{dens}(alpha )/A(h))</span>, where <i>h</i> is the largest integer such that <span>(alpha in K^{times h})</span> and <i>A</i>(<i>h</i>) is a suitable Artin constant, by varying <span>(alpha )</span> such that <span>(textrm{dens}(alpha )ne 0)</span>. We also provide optimal bounds by varying both <i>K</i> and <span>(alpha )</span>. Moreover, we obtain general formulae for <span>(textrm{dens}(alpha )/A(h))</span>.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"96 1","pages":"29 - 72"},"PeriodicalIF":0.2,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878053","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 order estimates of the q-analogue of the Riemann zeta function 黎曼ζ函数的q-类似函数的阶估计注记
IF 0.2 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2026-06-30 DOI: 10.1007/s12188-026-00298-y
Hideki Murahara, Tomokazu Onozuka
{"title":"A note on order estimates of the q-analogue of the Riemann zeta function","authors":"Hideki Murahara,&nbsp;Tomokazu Onozuka","doi":"10.1007/s12188-026-00298-y","DOIUrl":"10.1007/s12188-026-00298-y","url":null,"abstract":"<div><p>At the first step of studying order estimates for the <i>q</i>-analogue of the Riemann zeta function, we estimate bounds for it on vertical lines for a fixed parameter <i>q</i>.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"96 1","pages":"23 - 28"},"PeriodicalIF":0.2,"publicationDate":"2026-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878052","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 prime radical of ore extensions 关于矿扩展的素根
IF 0.2 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2026-06-22 DOI: 10.1007/s12188-026-00299-x
Marek Kȩpczyk
{"title":"On prime radical of ore extensions","authors":"Marek Kȩpczyk","doi":"10.1007/s12188-026-00299-x","DOIUrl":"10.1007/s12188-026-00299-x","url":null,"abstract":"<div><p>The results concern Ore ring extensions, including differential and skew polynomial extensions, with particular emphasis on the prime radical <span>(beta )</span>. It is shown that for an algebra <i>R</i> over a field with a locally algebraic endomorphism <span>(sigma )</span>, <span>(beta (R) subseteq beta (R[x; sigma ]))</span>. An analogous result is obtained for algebras of the form <span>(R[x; delta ])</span> with a locally algebraic derivation <span>(delta )</span>, provided that the prime radical <span>(beta (R))</span> is <span>(delta )</span>-stable.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"96 1","pages":"93 - 103"},"PeriodicalIF":0.2,"publicationDate":"2026-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-026-00299-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878055","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
Artin–Schreier quandles of involutions in absolute Galois groups 绝对伽罗瓦群中的Artin-Schreier纠缠
IF 0.2 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2026-05-06 DOI: 10.1007/s12188-026-00297-z
Markus Szymik
{"title":"Artin–Schreier quandles of involutions in absolute Galois groups","authors":"Markus Szymik","doi":"10.1007/s12188-026-00297-z","DOIUrl":"10.1007/s12188-026-00297-z","url":null,"abstract":"<div><p>We introduce a new invariant of fields that refines their real spectrum and is related to their absolute Galois group: the Artin–Schreier quandle. For totally real number fields, it is freely generated—in the variety of profinite involutory quandles—by a Cantor space of indeterminates. For Laurent series fields, we compute it in terms of the Artin–Schreier quandle of the coefficient field. This result, along with other examples, shows that, in general, there are relations.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"96 1","pages":"1 - 21"},"PeriodicalIF":0.2,"publicationDate":"2026-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-026-00297-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878056","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
Elliptic constant cycle curves on Kummer surfaces Kummer曲面上的椭圆常循环曲线
IF 0.2 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2026-04-13 DOI: 10.1007/s12188-026-00296-0
Jiexiang Huang
{"title":"Elliptic constant cycle curves on Kummer surfaces","authors":"Jiexiang Huang","doi":"10.1007/s12188-026-00296-0","DOIUrl":"10.1007/s12188-026-00296-0","url":null,"abstract":"<div>\u0000 \u0000 <p>The order of a constant cycle curve <span>(C subset X)</span> on a complex K3 surface, defined by Huybrechts, is a positive integer that measures the obstruction to decomposing the diagonal class <span>(Delta _C)</span> in the Chow group <span>(mathrm{CH}^2(X times C))</span>. In this paper, we compute the order of elliptic constant cycle curves that naturally arise on Kummer surfaces, by passing to the transcendental intermediate Jacobian <span>(J_{textrm{tr}}^3(X times C))</span>. As a consequence, every <span>(n in mathbb {N})</span> can be realized as the order of a constant cycle curve on a complex K3 surface.</p>\u0000 </div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"96 1","pages":"73 - 92"},"PeriodicalIF":0.2,"publicationDate":"2026-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-026-00296-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148878054","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
Decreasing subsequences and Viennot for oscillating tableaux 递减子序列和维恩诺振荡表
IF 0.3 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2026-03-16 DOI: 10.1007/s12188-026-00295-1
Elijah Bodish, Ben Elias, David E. V. Rose, Logan Tatham
{"title":"Decreasing subsequences and Viennot for oscillating tableaux","authors":"Elijah Bodish,&nbsp;Ben Elias,&nbsp;David E. V. Rose,&nbsp;Logan Tatham","doi":"10.1007/s12188-026-00295-1","DOIUrl":"10.1007/s12188-026-00295-1","url":null,"abstract":"<div>\u0000 \u0000 <p>We establish an extension of Viennot’s geometric (shadow line) construction to the setting of oscillating tableaux. We then use this to give a new proof of the Type <i>C</i> analogue of Schensted’s theorem on longest decreasing subsequences. This pairs with our results from [3] on Type <i>C</i> webs to give a direct proof of a result of Sundaram and Stanley: that the dimension of the space of invariant vectors in a 2<i>k</i>-fold tensor product of the vector representation of <span>(mathfrak {sp}_{2n})</span> equals the number of <span>((n+1))</span>-avoiding matchings of 2<i>k</i> points.</p>\u0000 </div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"95 2","pages":"161 - 179"},"PeriodicalIF":0.3,"publicationDate":"2026-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-026-00295-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147560184","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
Artin formalism for p-adic L-functions of weight-two modular forms at non-ordinary primes 非普通素数处权模形式的p进l函数的Artin形式
IF 0.3 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2026-01-02 DOI: 10.1007/s12188-025-00294-8
Antonio Lei
{"title":"Artin formalism for p-adic L-functions of weight-two modular forms at non-ordinary primes","authors":"Antonio Lei","doi":"10.1007/s12188-025-00294-8","DOIUrl":"10.1007/s12188-025-00294-8","url":null,"abstract":"<div><p>Let <i>p</i> be an odd prime number. Let <i>f</i> be a weight-two normalized Hecke eigen-cuspform that is non-ordinary at <i>p</i>. Let <i>K</i> be an imaginary quadratic field in which <i>p</i> splits. We study the Artin formalism for the two-variable signed <i>p</i>-adic <i>L</i>-functions attached to <i>f</i> over <i>K</i>. In particular, we give evidence of a prediction made by Castella–Ciperiani–Skinner–Sprung and provide a different proof of (Sprung in Adv Math 449:109741, 2024, Lemma 4.34).</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"95 2","pages":"149 - 160"},"PeriodicalIF":0.3,"publicationDate":"2026-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559061","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
Fine Selmer groups of modular forms 模形式的精细Selmer群
IF 0.3 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2025-11-28 DOI: 10.1007/s12188-025-00292-w
Sören Kleine, Katharina Müller
{"title":"Fine Selmer groups of modular forms","authors":"Sören Kleine,&nbsp;Katharina Müller","doi":"10.1007/s12188-025-00292-w","DOIUrl":"10.1007/s12188-025-00292-w","url":null,"abstract":"<div><p>We compare the Iwasawa invariants of fine Selmer groups of <i>p</i>-adic Galois representations over admissible <i>p</i>-adic Lie extensions of a number field <i>K</i> to the Iwasawa invariants of ideal class groups along these Lie extensions. More precisely, let <i>K</i> be a number field, let <i>V</i> be a <i>p</i>-adic representation of the absolute Galois group <span>(G_K)</span> of <i>K</i>, and choose a <span>(G_K)</span>-invariant lattice <span>({T subseteq V})</span>. We study the fine Selmer groups of <span>({A = V/T})</span> over suitable <i>p</i>-adic Lie extensions <span>(K_infty /K)</span>, comparing their corank and <span>(mu )</span>-invariant to the corank and the <span>(mu )</span>-invariant of the Iwasawa module of ideal class groups in <span>(K_infty /K)</span>. In the second part of the article, we compare the Iwasawa <span>(mu )</span>- and <span>(l_0)</span>-invariants of the fine Selmer groups of CM modular forms on the one hand and the Iwasawa invariants of ideal class groups on the other hand over trivialising multiple <span>(mathbb {Z}_p)</span>-extensions of <i>K</i>.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"95 2","pages":"93 - 121"},"PeriodicalIF":0.3,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-025-00292-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147562014","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
Sequences of integers generated by two fixed primes 由两个固定素数生成的整数序列
IF 0.3 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2025-11-24 DOI: 10.1007/s12188-025-00293-9
Alessandro Languasco, Florian Luca, Pieter Moree, Alain Togbé
{"title":"Sequences of integers generated by two fixed primes","authors":"Alessandro Languasco,&nbsp;Florian Luca,&nbsp;Pieter Moree,&nbsp;Alain Togbé","doi":"10.1007/s12188-025-00293-9","DOIUrl":"10.1007/s12188-025-00293-9","url":null,"abstract":"<div><p>Let <i>p</i> and <i>q</i> be two distinct fixed prime numbers and <span>((n_i)_{ige 0})</span> the sequence of consecutive integers of the form <span>(p^acdot q^b)</span> with <span>(a,bge 0)</span>. Tijdeman gave a lower bound (1973) and an upper bound (1974) for the gap size <span>(n_{i+1}-n_i)</span>, with each bound containing an unspecified exponent and implicit constant. We will explicitly bound these four quantities. Earlier Langevin (1976) gave weaker estimates for (only) the exponents. Given a real number <span>(alpha &gt;1)</span>, there exists a smallest number <i>m</i> such that for every <span>(nge m)</span>, there exists an integer <span>(n_i)</span> in <span>([n,nalpha ))</span>. Our effective version of Tijdeman’s result immediately implies an upper bound for <i>m</i>, which using the Koksma–Erdős–Turan inequality we will improve on. We present a fast algorithm to determine <i>m</i> when <span>(max {p,q})</span> is not too large and demonstrate it with numerical material. In an appendix we explain, given <span>(n_i)</span>, how to efficiently determine both <span>(n_{i-1})</span> and <span>(n_{i+1})</span>, something closely related to work of Bérczes, Dujella and Hajdu.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"95 2","pages":"123 - 148"},"PeriodicalIF":0.3,"publicationDate":"2025-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-025-00293-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561085","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
Abelian versus triangulated quotients 阿贝尔商与三角商
IF 0.3 4区 数学
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2025-08-13 DOI: 10.1007/s12188-025-00291-x
Henning Krause
{"title":"Abelian versus triangulated quotients","authors":"Henning Krause","doi":"10.1007/s12188-025-00291-x","DOIUrl":"10.1007/s12188-025-00291-x","url":null,"abstract":"<div><p>It is shown that any localisation of triangulated categories induces (up to an equivalence) a localisation of abelian categories when one passes to their abelianisations. From this one obtains for any enlargement of Grothendieck universes an example of an abelian category and a Serre subcategory within the smaller universe such that the corresponding quotient does only exist within the bigger universe. The second part of this note provides an analogue for the abelian hull of an arbitrary category.</p></div>","PeriodicalId":50932,"journal":{"name":"Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg","volume":"95 2","pages":"181 - 187"},"PeriodicalIF":0.3,"publicationDate":"2025-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s12188-025-00291-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559535","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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