Pub Date : 2024-01-16DOI: 10.1007/s44007-023-00083-w
Seda Karateke, M. Zontul, Vishnu Narayan Mishra, A. R. Gairola
{"title":"On the Approximation by Stancu-Type Bivariate Jakimovski–Leviatan–Durrmeyer Operators","authors":"Seda Karateke, M. Zontul, Vishnu Narayan Mishra, A. R. Gairola","doi":"10.1007/s44007-023-00083-w","DOIUrl":"https://doi.org/10.1007/s44007-023-00083-w","url":null,"abstract":"","PeriodicalId":74051,"journal":{"name":"La matematica","volume":"42 35","pages":"1-23"},"PeriodicalIF":0.0,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139528217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-29DOI: 10.1007/s44007-023-00074-x
Jane H. Long
{"title":"Cohomology Classes of Qd(3)","authors":"Jane H. Long","doi":"10.1007/s44007-023-00074-x","DOIUrl":"https://doi.org/10.1007/s44007-023-00074-x","url":null,"abstract":"","PeriodicalId":74051,"journal":{"name":"La matematica","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139210335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-29DOI: 10.1007/s44007-023-00073-y
Jane H. Long
{"title":"Cohomology Classes of the Qd(p) Groups","authors":"Jane H. Long","doi":"10.1007/s44007-023-00073-y","DOIUrl":"https://doi.org/10.1007/s44007-023-00073-y","url":null,"abstract":"","PeriodicalId":74051,"journal":{"name":"La matematica","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139213788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-20DOI: 10.1007/s44007-023-00078-7
Christina Frederick, Karamatou Yacoubou Djima
{"title":"Examples of Riesz Bases of Exponentials for Multi-tiling Domains and Their Duals","authors":"Christina Frederick, Karamatou Yacoubou Djima","doi":"10.1007/s44007-023-00078-7","DOIUrl":"https://doi.org/10.1007/s44007-023-00078-7","url":null,"abstract":"","PeriodicalId":74051,"journal":{"name":"La matematica","volume":"14 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139255332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-10DOI: 10.1007/s44007-023-00067-w
Jürgen Klüners, Jiuya Wang
For odd primes $$ell $$ and number fields k, we study the asymptotic distribution of number fields L/k given as a tower of relative cyclic $$C_ell $$ -extensions L/F/k using the idélic approach of class field theory. This involves a classification for the Galois group of L/k based on local conditions on L/F and F/k, and an extension of the method of Wright in enumerating abelian extensions. We call the possible Galois groups for these extensions generalized and twisted Heisenberg groups. We then prove the strong Malle–conjecture for all these groups in their representation on $$ell ^2$$ points.
{"title":"Idélic Approach in Enumerating Heisenberg Extensions","authors":"Jürgen Klüners, Jiuya Wang","doi":"10.1007/s44007-023-00067-w","DOIUrl":"https://doi.org/10.1007/s44007-023-00067-w","url":null,"abstract":"For odd primes $$ell $$ and number fields k, we study the asymptotic distribution of number fields L/k given as a tower of relative cyclic $$C_ell $$ -extensions L/F/k using the idélic approach of class field theory. This involves a classification for the Galois group of L/k based on local conditions on L/F and F/k, and an extension of the method of Wright in enumerating abelian extensions. We call the possible Galois groups for these extensions generalized and twisted Heisenberg groups. We then prove the strong Malle–conjecture for all these groups in their representation on $$ell ^2$$ points.","PeriodicalId":74051,"journal":{"name":"La matematica","volume":"121 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135136356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-11-10DOI: 10.1007/s44007-023-00075-w
Anwita Bhowmik, Rupam Barman
For a prime $$pequiv 3pmod 4$$ and a positive integer t, let $$q=p^{2t}$$ . The Peisert graph of order q is the graph with vertex set $$mathbb {F}_q$$ such that ab is an edge if $$a-bin langle g^4rangle cup glangle g^4rangle $$ , where g is a primitive element of $$mathbb {F}_q$$ . In this paper, we construct a similar graph with vertex set as the commutative ring $$mathbb {Z}_n$$ for suitable n, which we call Peisert-like graph and denote by $$G^*(n)$$ . Owing to the need for cyclicity of the group of units of $$mathbb {Z}_n$$ , we consider $$n=p^alpha $$ or $$2p^alpha $$ , where $$pequiv 1pmod 4$$ is a prime and $$alpha $$ is a positive integer. For primes $$pequiv 1pmod 8$$ , we compute the number of triangles in the graph $$G^*(p^{alpha })$$ by evaluating certain character sums. Next, we study cliques of order 4 in $$G^*(p^{alpha })$$ . To find the number of cliques of order 4 in $$G^*(p^{alpha })$$ , we first introduce hypergeometric functions containing Dirichlet characters as arguments and then express the number of cliques of order 4 in $$G^*(p^{alpha })$$ in terms of these hypergeometric functions.
{"title":"Hypergeometric Functions for Dirichlet Characters and Peisert-Like Graphs on $$mathbb {Z}_n$$","authors":"Anwita Bhowmik, Rupam Barman","doi":"10.1007/s44007-023-00075-w","DOIUrl":"https://doi.org/10.1007/s44007-023-00075-w","url":null,"abstract":"For a prime $$pequiv 3pmod 4$$ and a positive integer t, let $$q=p^{2t}$$ . The Peisert graph of order q is the graph with vertex set $$mathbb {F}_q$$ such that ab is an edge if $$a-bin langle g^4rangle cup glangle g^4rangle $$ , where g is a primitive element of $$mathbb {F}_q$$ . In this paper, we construct a similar graph with vertex set as the commutative ring $$mathbb {Z}_n$$ for suitable n, which we call Peisert-like graph and denote by $$G^*(n)$$ . Owing to the need for cyclicity of the group of units of $$mathbb {Z}_n$$ , we consider $$n=p^alpha $$ or $$2p^alpha $$ , where $$pequiv 1pmod 4$$ is a prime and $$alpha $$ is a positive integer. For primes $$pequiv 1pmod 8$$ , we compute the number of triangles in the graph $$G^*(p^{alpha })$$ by evaluating certain character sums. Next, we study cliques of order 4 in $$G^*(p^{alpha })$$ . To find the number of cliques of order 4 in $$G^*(p^{alpha })$$ , we first introduce hypergeometric functions containing Dirichlet characters as arguments and then express the number of cliques of order 4 in $$G^*(p^{alpha })$$ in terms of these hypergeometric functions.","PeriodicalId":74051,"journal":{"name":"La matematica","volume":" 13","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135141136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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