Research in the Mathematical Sciences最新文献

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Hochschild cohomology of symmetric groups and generating functions, II 对称群与生成函数的Hochschild上同调,2
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2023-01-09 DOI: 10.1007/s40687-023-00382-2
Dave Benson, R. Kessar, M. Linckelmann
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引用次数: 1
Modular knots, automorphic forms, and the Rademacher symbols for triangle groups. 模结,自同构形式,三角群的Rademacher符号。
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2023-01-01 DOI: 10.1007/s40687-022-00366-8
Toshiki Matsusaka, Jun Ueki
{"title":"Modular knots, automorphic forms, and the Rademacher symbols for triangle groups.","authors":"Toshiki Matsusaka,&nbsp;Jun Ueki","doi":"10.1007/s40687-022-00366-8","DOIUrl":"https://doi.org/10.1007/s40687-022-00366-8","url":null,"abstract":"<p><p>É. Ghys proved that the linking numbers of modular knots and the \"missing\" trefoil <math><msub><mi>K</mi> <mrow><mn>2</mn> <mo>,</mo> <mn>3</mn></mrow> </msub> </math> in <math><msup><mi>S</mi> <mn>3</mn></msup> </math> coincide with the values of a highly ubiquitous function called the Rademacher symbol for <math> <mrow><msub><mtext>SL</mtext> <mn>2</mn></msub> <mi>Z</mi></mrow> </math> . In this article, we replace <math> <mrow><msub><mtext>SL</mtext> <mn>2</mn></msub> <mi>Z</mi> <mo>=</mo> <msub><mi>Γ</mi> <mrow><mn>2</mn> <mo>,</mo> <mn>3</mn></mrow> </msub> </mrow> </math> by the triangle group <math><msub><mi>Γ</mi> <mrow><mi>p</mi> <mo>,</mo> <mi>q</mi></mrow> </msub> </math> for any coprime pair (<i>p</i>, <i>q</i>) of integers with <math><mrow><mn>2</mn> <mo>≤</mo> <mi>p</mi> <mo><</mo> <mi>q</mi></mrow> </math> . We invoke the theory of harmonic Maass forms for <math><msub><mi>Γ</mi> <mrow><mi>p</mi> <mo>,</mo> <mi>q</mi></mrow> </msub> </math> to introduce the notion of the Rademacher symbol <math><msub><mi>ψ</mi> <mrow><mi>p</mi> <mo>,</mo> <mi>q</mi></mrow> </msub> </math> , and provide several characterizations. Among other things, we generalize Ghys's theorem for modular knots around any \"missing\" torus knot <math><msub><mi>K</mi> <mrow><mi>p</mi> <mo>,</mo> <mi>q</mi></mrow> </msub> </math> in <math><msup><mi>S</mi> <mn>3</mn></msup> </math> and in a lens space.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"10 1","pages":"4"},"PeriodicalIF":1.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9734963/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10382569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 4
The Bloch–Okounkov theorem for congruence subgroups and Taylor coefficients of quasi-Jacobi forms 拟jacobi形式的同余子群和Taylor系数的Bloch-Okounkov定理
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2022-12-14 DOI: 10.1007/s40687-022-00369-5
Jan-Willem M. van Ittersum
{"title":"The Bloch–Okounkov theorem for congruence subgroups and Taylor coefficients of quasi-Jacobi forms","authors":"Jan-Willem M. van Ittersum","doi":"10.1007/s40687-022-00369-5","DOIUrl":"https://doi.org/10.1007/s40687-022-00369-5","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"11 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73891918","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: 2
High-dimensional density estimation with tensorizing flow 基于张紧流的高维密度估计
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2022-12-01 DOI: 10.1007/s40687-023-00395-x
Yinuo Ren, Hongli Zhao, Y. Khoo, Lexing Ying
{"title":"High-dimensional density estimation with tensorizing flow","authors":"Yinuo Ren, Hongli Zhao, Y. Khoo, Lexing Ying","doi":"10.1007/s40687-023-00395-x","DOIUrl":"https://doi.org/10.1007/s40687-023-00395-x","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"53 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85731071","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: 4
Serre duality for tame Deligne–Mumford stacks 为驯服的delign - mumford堆栈提供二元性
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2022-11-19 DOI: 10.1007/s40687-022-00367-7
Denis Levchenko
{"title":"Serre duality for tame Deligne–Mumford stacks","authors":"Denis Levchenko","doi":"10.1007/s40687-022-00367-7","DOIUrl":"https://doi.org/10.1007/s40687-022-00367-7","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"80 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88277208","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: 1
The algebraic parts of the central values of quadratic twists of modular L-functions modulo $$ell $$ 模l函数的二次扭转中心值的代数部分 $$ell $$
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2022-11-02 DOI: 10.1007/s40687-022-00361-z
D. Choi, Youngmin Lee
{"title":"The algebraic parts of the central values of quadratic twists of modular L-functions modulo $$ell $$","authors":"D. Choi, Youngmin Lee","doi":"10.1007/s40687-022-00361-z","DOIUrl":"https://doi.org/10.1007/s40687-022-00361-z","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"8 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88551866","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
Operator theory on generalized Hartogs triangles 广义Hartogs三角形的算子理论
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2022-10-12 DOI: 10.1007/s40687-023-00397-9
S. Chavan, Shubham Jain, Paramita Pramanick
{"title":"Operator theory on generalized Hartogs triangles","authors":"S. Chavan, Shubham Jain, Paramita Pramanick","doi":"10.1007/s40687-023-00397-9","DOIUrl":"https://doi.org/10.1007/s40687-023-00397-9","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"8 12 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89675964","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
$${}_{4}F_{3}$$-Gaussian hypergeometric series and traces of Frobenius for elliptic curves $${}_{4}F_{3}$$椭圆曲线的-高斯超几何级数和Frobenius迹
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2022-10-05 DOI: 10.1007/s40687-022-00358-8
M. Tripathi, J. Meher
{"title":"$${}_{4}F_{3}$$-Gaussian hypergeometric series and traces of Frobenius for elliptic curves","authors":"M. Tripathi, J. Meher","doi":"10.1007/s40687-022-00358-8","DOIUrl":"https://doi.org/10.1007/s40687-022-00358-8","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"108 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90075310","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: 1
Performance assessment of the maximum likelihood ensemble filter and the ensemble Kalman filters for nonlinear problems 非线性问题的最大似然集合滤波器和集合卡尔曼滤波器的性能评价
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2022-10-03 DOI: 10.1007/s40687-022-00359-7
Yijun Wang, M. Zupanski, Xuemin Tu, Xinfeng Gao
{"title":"Performance assessment of the maximum likelihood ensemble filter and the ensemble Kalman filters for nonlinear problems","authors":"Yijun Wang, M. Zupanski, Xuemin Tu, Xinfeng Gao","doi":"10.1007/s40687-022-00359-7","DOIUrl":"https://doi.org/10.1007/s40687-022-00359-7","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"5 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80174167","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
Derivatives of L-series of weakly holomorphic cusp forms 弱全纯尖形l级数的导数
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2022-09-19 DOI: 10.1007/s40687-022-00363-x
Nikolaos Diamantis, Fredrik Strömberg
{"title":"Derivatives of L-series of weakly holomorphic cusp forms","authors":"Nikolaos Diamantis, Fredrik Strömberg","doi":"10.1007/s40687-022-00363-x","DOIUrl":"https://doi.org/10.1007/s40687-022-00363-x","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"9 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87344224","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
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