Pub Date : 2024-09-01DOI: 10.1080/10586458.2024.2379797
Herbert Gangl, Paul E. Gunnells, Jonathan Hanke, Dan Yasaki
We report on computations of the cohomology of GL2(OD) and SL2(OD) , where D < 0 is a fundamental discriminant. These computations go well beyond earlier results of Vogtmann and Scheutzow. We us...
我们报告了 GL2(OD) 和 SL2(OD) 的同调计算，其中 D < 0 是基本判别式。这些计算远远超出了沃格特曼和舍伊佐夫的早期结果。我们...
{"title":"On the Cohomology of GL2 and SL2 over Imaginary Quadratic Fields","authors":"Herbert Gangl, Paul E. Gunnells, Jonathan Hanke, Dan Yasaki","doi":"10.1080/10586458.2024.2379797","DOIUrl":"https://doi.org/10.1080/10586458.2024.2379797","url":null,"abstract":"We report on computations of the cohomology of GL2(OD) and SL2(OD) , where D < 0 is a fundamental discriminant. These computations go well beyond earlier results of Vogtmann and Scheutzow. We us...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192754","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}
Pub Date : 2024-08-18DOI: 10.1080/10586458.2024.2381676
Alexander Goncharov, Yaman Paksoy
We evaluate the values of the Lebesgue constants in polynomial interpolation for three types of Cantor sets. In all cases, the sequences of Lebesgue constants are not bounded. This disproves the st...
我们评估了三种 Cantor 集的多项式插值中的 Lebesgue 常量值。在所有情况下，Lebesgue常数序列都没有边界。这推翻了...
{"title":"Lebesgue Constants for Cantor Sets","authors":"Alexander Goncharov, Yaman Paksoy","doi":"10.1080/10586458.2024.2381676","DOIUrl":"https://doi.org/10.1080/10586458.2024.2381676","url":null,"abstract":"We evaluate the values of the Lebesgue constants in polynomial interpolation for three types of Cantor sets. In all cases, the sequences of Lebesgue constants are not bounded. This disproves the st...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192755","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}
Pub Date : 2024-08-12DOI: 10.1080/10586458.2024.2379799
Richard Ehrenborg
We are interested in conjecturing the sign of the pizza quantity P(H,B(a,R)) for the irreducible Coxeter arrangements H of type An , where n≡2 or 3 mod 4 , and type Dn , where n is odd. Our appr...
我们有兴趣猜测 An 型（n≡2 或 3 mod 4）和 Dn 型（n 为奇数）不可还原柯克赛特排列 H 的比萨量 P(H,B(a,R)) 的符号。我们的应用...
{"title":"Conjectures for Cutting Pizza with Coxeter Arrangements","authors":"Richard Ehrenborg","doi":"10.1080/10586458.2024.2379799","DOIUrl":"https://doi.org/10.1080/10586458.2024.2379799","url":null,"abstract":"We are interested in conjecturing the sign of the pizza quantity P(H,B(a,R)) for the irreducible Coxeter arrangements H of type An , where n≡2 or 3 mod 4 , and type Dn , where n is odd. Our appr...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192756","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}
Pub Date : 2024-08-12DOI: 10.1080/10586458.2024.2379802
Marinko Ž. Timotijević, Rade T. Živaljević, Filip D. Jevtić
The Bier sphere Bier(G)=Bier(K):=K∗ΔK° and the canonical fan Fan(Γ)=Fan(K) are combinatorial/geometric companions of a simple game G=(P,Γ) (equivalently the associated simplicial complex K), whe...
{"title":"Polytopality of Simple Games","authors":"Marinko Ž. Timotijević, Rade T. Živaljević, Filip D. Jevtić","doi":"10.1080/10586458.2024.2379802","DOIUrl":"https://doi.org/10.1080/10586458.2024.2379802","url":null,"abstract":"The Bier sphere Bier(G)=Bier(K):=K∗ΔK° and the canonical fan Fan(Γ)=Fan(K) are combinatorial/geometric companions of a simple game G=(P,Γ) (equivalently the associated simplicial complex K), whe...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142192757","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}
Pub Date : 2024-08-08DOI: 10.1080/10586458.2024.2382362
Torre Caparatta, Sebastian Pauli, Filip Saidak
We investigate the behavior of fractional derivatives of polynomials. In particular, we consider the locations and the asymptotic behavior of their zeros and give bounds for their Mahler measure.
{"title":"Zeros of Fractional Derivatives of Polynomials","authors":"Torre Caparatta, Sebastian Pauli, Filip Saidak","doi":"10.1080/10586458.2024.2382362","DOIUrl":"https://doi.org/10.1080/10586458.2024.2382362","url":null,"abstract":"We investigate the behavior of fractional derivatives of polynomials. In particular, we consider the locations and the asymptotic behavior of their zeros and give bounds for their Mahler measure.","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141932541","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}
Pub Date : 2024-08-06DOI: 10.1080/10586458.2024.2380794
Andrei Constantin
This paper explores the possibility of constructing multivariate generating functions for all cohomology dimensions of all holomorphic line bundles on certain complex projective varieties of Fano, ...
本文探讨了在某些复杂投影的法诺、...
{"title":"Generating Functions for Line Bundle Cohomology Dimensions on Complex Projective Varieties","authors":"Andrei Constantin","doi":"10.1080/10586458.2024.2380794","DOIUrl":"https://doi.org/10.1080/10586458.2024.2380794","url":null,"abstract":"This paper explores the possibility of constructing multivariate generating functions for all cohomology dimensions of all holomorphic line bundles on certain complex projective varieties of Fano, ...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141932543","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}
Pub Date : 2024-08-04DOI: 10.1080/10586458.2024.2379792
Robert Evans, Daniel Macias Castillo, Hanneke Wiersema
Let A/Q be a Jacobian variety and let F be a totally real, tamely ramified, abelian number field. Given a character ψ of F/Q, Deligne’s Period Conjecture asserts the algebraicity of the suitably no...
设 A/Q 是雅各布综，设 F 是一个完全实数、驯服地夯实的阿贝尔数域。给定 F/Q 的一个字符 ψ，德莱尼周期猜想断言了适当无...
{"title":"Numerical Evidence for a Refinement of Deligne’s Period Conjecture for Jacobians of Curves","authors":"Robert Evans, Daniel Macias Castillo, Hanneke Wiersema","doi":"10.1080/10586458.2024.2379792","DOIUrl":"https://doi.org/10.1080/10586458.2024.2379792","url":null,"abstract":"Let A/Q be a Jacobian variety and let F be a totally real, tamely ramified, abelian number field. Given a character ψ of F/Q, Deligne’s Period Conjecture asserts the algebraicity of the suitably no...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141932542","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}
Pub Date : 2024-08-04DOI: 10.1080/10586458.2024.2382361
Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver, Alexey Pozdnyakov
We investigate the average value of the Frobenius trace at p over elliptic curves in a fixed conductor range with given rank. Plotting this average as p varies over the primes yields a striking osc...
我们研究了在给定秩的固定导体范围内的椭圆曲线上 p 处的弗罗贝尼斯迹的平均值。将这个平均值绘制成 p 在素数上的变化曲线，会产生一个惊人的振荡......
{"title":"Murmurations of Elliptic Curves","authors":"Yang-Hui He, Kyu-Hwan Lee, Thomas Oliver, Alexey Pozdnyakov","doi":"10.1080/10586458.2024.2382361","DOIUrl":"https://doi.org/10.1080/10586458.2024.2382361","url":null,"abstract":"We investigate the average value of the Frobenius trace at p over elliptic curves in a fixed conductor range with given rank. Plotting this average as p varies over the primes yields a striking osc...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141932651","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}
Pub Date : 2024-08-01DOI: 10.1080/10586458.2024.2379793
Alin Bostan, Frédéric Chapoton
Using an experimental mathematics approach, new relations are obtained between Dirichlet-like series for certain periodic coefficients and the moments of certain families of orthogonal polynomials....
利用实验数学方法，获得了某些周期系数的类狄利克列数列与某些正交多项式族的矩之间的新关系....
{"title":"Continued Fractions, Orthogonal Polynomials and Dirichlet Series","authors":"Alin Bostan, Frédéric Chapoton","doi":"10.1080/10586458.2024.2379793","DOIUrl":"https://doi.org/10.1080/10586458.2024.2379793","url":null,"abstract":"Using an experimental mathematics approach, new relations are obtained between Dirichlet-like series for certain periodic coefficients and the moments of certain families of orthogonal polynomials....","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141932546","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}
Pub Date : 2024-08-01DOI: 10.1080/10586458.2024.2381212
Xin Li, Liping Zhang, Yifen Ke
In this paper, a classical deflation process raised by Dayton, Li and Zeng is realized for the Brent equations, which provides new bounds for local dimensions of the solution set. Originally, this ...
{"title":"Deflation Conjecture and Local Dimensions of Brent Equations","authors":"Xin Li, Liping Zhang, Yifen Ke","doi":"10.1080/10586458.2024.2381212","DOIUrl":"https://doi.org/10.1080/10586458.2024.2381212","url":null,"abstract":"In this paper, a classical deflation process raised by Dayton, Li and Zeng is realized for the Brent equations, which provides new bounds for local dimensions of the solution set. Originally, this ...","PeriodicalId":50464,"journal":{"name":"Experimental Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141886230","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}
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