{"title":"Notes on compactness in $L^p$-spaces on locally compact groups","authors":"M. Krukowski","doi":"10.5565/publmat6722308","DOIUrl":"https://doi.org/10.5565/publmat6722308","url":null,"abstract":"","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48644827","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}
: We prove an explicit formula for the second moment of symmetric square L -functions associated to Maass forms for the full modular group. In particular, we show how to express the considered second moment in terms of dual second moments of symmetric square L -functions associated to Maass cusp forms of levels 4, 16, and 64.
{"title":"An explicit formula for the second moment of Maass form symmetric square $L$-functions","authors":"Olga Balkanova, D. Frolenkov","doi":"10.5565/publmat6722306","DOIUrl":"https://doi.org/10.5565/publmat6722306","url":null,"abstract":": We prove an explicit formula for the second moment of symmetric square L -functions associated to Maass forms for the full modular group. In particular, we show how to express the considered second moment in terms of dual second moments of symmetric square L -functions associated to Maass cusp forms of levels 4, 16, and 64.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44164643","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}
{"title":"$mathbb{Q}$-curves, Hecke characters and some Diophantine equations II","authors":"Ariel Pacetti, Lucas Villagra Torcomian","doi":"10.5565/publmat6722304","DOIUrl":"https://doi.org/10.5565/publmat6722304","url":null,"abstract":"","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135210121","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}
: Some crystalline measures supported by a Delone set Λ ⊂ R 2 are constructed in this note. This gives a new proof of a remarkable theorem by Pavel Kurasov and Peter Sarnak. 2020 Mathematics Subject Classification: Primary: 42A32; Secondary: 43A46.
{"title":"Crystalline measures in two dimensions","authors":"Y. Meyer","doi":"10.5565/publmat6712310","DOIUrl":"https://doi.org/10.5565/publmat6712310","url":null,"abstract":": Some crystalline measures supported by a Delone set Λ ⊂ R 2 are constructed in this note. This gives a new proof of a remarkable theorem by Pavel Kurasov and Peter Sarnak. 2020 Mathematics Subject Classification: Primary: 42A32; Secondary: 43A46.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48857856","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}
Cristóbal Gil Canto, D. Martín Barquero, C. Martín González
: It is known that the ideals of a Leavitt path algebra L K ( E ) generated by P l ( E ), by P c ( E ), or by P ec ( E ) are invariant under isomorphism. Though the ideal generated by P b ∞ ( E ) is not invariant we find its “natural” replacement (which is indeed invariant): the one generated by the vertices of P b ∞ p (vertices with pure in-finite bifurcations). We also give some procedures to construct invariant ideals from previous known invariant ideals. One of these procedures involves topology, so we introduce the DCC topology and relate it to annihilators in the algebraic counterpart of the work. To be more explicit: if H is a hereditary saturated subset of vertices providing an invariant ideal, its exterior ext( H ) in the DCC topology of E 0 generates a new invariant ideal. The other constructor of invariant ideals is more categorical in nature. Some hereditary sets can be seen as functors from graphs to sets (for instance P l , etc.). Thus a second method emerges from the possibility of applying the induced functor to the quotient graph. The easiest example is the known socle chain Soc (1) ( ) ⊆ Soc (2) ( ) ⊆ ··· , all of which are proved to be invariant. We generalize this idea to any hereditary and saturated invariant functor. Finally we investigate a kind of composition of hereditary and saturated functors which is associative.
{"title":"Invariant ideals in Leavitt path algebras","authors":"Cristóbal Gil Canto, D. Martín Barquero, C. Martín González","doi":"10.5565/publmat6622203","DOIUrl":"https://doi.org/10.5565/publmat6622203","url":null,"abstract":": It is known that the ideals of a Leavitt path algebra L K ( E ) generated by P l ( E ), by P c ( E ), or by P ec ( E ) are invariant under isomorphism. Though the ideal generated by P b ∞ ( E ) is not invariant we find its “natural” replacement (which is indeed invariant): the one generated by the vertices of P b ∞ p (vertices with pure in-finite bifurcations). We also give some procedures to construct invariant ideals from previous known invariant ideals. One of these procedures involves topology, so we introduce the DCC topology and relate it to annihilators in the algebraic counterpart of the work. To be more explicit: if H is a hereditary saturated subset of vertices providing an invariant ideal, its exterior ext( H ) in the DCC topology of E 0 generates a new invariant ideal. The other constructor of invariant ideals is more categorical in nature. Some hereditary sets can be seen as functors from graphs to sets (for instance P l , etc.). Thus a second method emerges from the possibility of applying the induced functor to the quotient graph. The easiest example is the known socle chain Soc (1) ( ) ⊆ Soc (2) ( ) ⊆ ··· , all of which are proved to be invariant. We generalize this idea to any hereditary and saturated invariant functor. Finally we investigate a kind of composition of hereditary and saturated functors which is associative.","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44845520","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}
. We give an estimate that quantifies the fact that a normalized quasi-conformal map whose dilatation is non-zero only on a set of small area approximates the identity uniformly on the whole plane. The precise statement is motivated by applications of the author’s quasiconformal folding method for constructing entire functions; in particular a construction of transcendental wandering domains given by Fagella, Godillon and Jarque [7].
{"title":"Quasiconformal maps with thin dilatations","authors":"C. Bishop","doi":"10.5565/publmat6622207","DOIUrl":"https://doi.org/10.5565/publmat6622207","url":null,"abstract":". We give an estimate that quantifies the fact that a normalized quasi-conformal map whose dilatation is non-zero only on a set of small area approximates the identity uniformly on the whole plane. The precise statement is motivated by applications of the author’s quasiconformal folding method for constructing entire functions; in particular a construction of transcendental wandering domains given by Fagella, Godillon and Jarque [7].","PeriodicalId":54531,"journal":{"name":"Publicacions Matematiques","volume":" ","pages":""},"PeriodicalIF":1.1,"publicationDate":"2022-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45123971","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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