Pub Date : 2023-01-30DOI: 10.1007/s40687-023-00375-1
Aditi Savalia, A. Vatwani
{"title":"Limitations to equidistribution in arithmetic progressions","authors":"Aditi Savalia, A. Vatwani","doi":"10.1007/s40687-023-00375-1","DOIUrl":"https://doi.org/10.1007/s40687-023-00375-1","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"16 1","pages":"1-39"},"PeriodicalIF":1.2,"publicationDate":"2023-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87239526","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}
Pub Date : 2023-01-23DOI: 10.1007/s40687-022-00372-w
Savin Treanțǎ, Yating Guo
{"title":"The study of certain optimization problems via variational inequalities","authors":"Savin Treanțǎ, Yating Guo","doi":"10.1007/s40687-022-00372-w","DOIUrl":"https://doi.org/10.1007/s40687-022-00372-w","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"8 1","pages":"1-13"},"PeriodicalIF":1.2,"publicationDate":"2023-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87033769","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}
Pub Date : 2023-01-09DOI: 10.1007/s40687-023-00382-2
Dave Benson, R. Kessar, M. Linckelmann
{"title":"Hochschild cohomology of symmetric groups and generating functions, II","authors":"Dave Benson, R. Kessar, M. Linckelmann","doi":"10.1007/s40687-023-00382-2","DOIUrl":"https://doi.org/10.1007/s40687-023-00382-2","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"39 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85183666","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}
Pub Date : 2023-01-01DOI: 10.1007/s40687-022-00366-8
Toshiki Matsusaka, Jun Ueki
É. Ghys proved that the linking numbers of modular knots and the "missing" trefoil in coincide with the values of a highly ubiquitous function called the Rademacher symbol for . In this article, we replace by the triangle group for any coprime pair (p, q) of integers with . We invoke the theory of harmonic Maass forms for to introduce the notion of the Rademacher symbol , and provide several characterizations. Among other things, we generalize Ghys's theorem for modular knots around any "missing" torus knot in and in a lens space.
{"title":"Modular knots, automorphic forms, and the Rademacher symbols for triangle groups.","authors":"Toshiki Matsusaka, 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}
Pub Date : 2022-12-14DOI: 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}
Pub Date : 2022-12-01DOI: 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}
Pub Date : 2022-11-19DOI: 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}
Pub Date : 2022-11-02DOI: 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}
Pub Date : 2022-10-12DOI: 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}
Pub Date : 2022-10-05DOI: 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}
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