Pub Date : 2024-09-02DOI: 10.1016/j.indag.2024.09.001
Fritz Schweiger
Here we consider piecewise fractional linear maps with three branches. The paper presents a study of invariant measures with densities which can be written as infinite series. These series either have infinitely many poles or they sum up to a function with just one pole.
{"title":"On Moebius maps which are characterized by the configuration of their dual maps","authors":"Fritz Schweiger","doi":"10.1016/j.indag.2024.09.001","DOIUrl":"https://doi.org/10.1016/j.indag.2024.09.001","url":null,"abstract":"Here we consider piecewise fractional linear maps with three branches. The paper presents a study of invariant measures with densities which can be written as infinite series. These series either have infinitely many poles or they sum up to a function with just one pole.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180747","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 : 2024-09-02DOI: 10.1016/j.indag.2024.08.006
Derong Kong, Beibei Sun
Given , the four corner Cantor set is a self-similar set generated by the iterated function system For let be the orthogonal projection of onto a line with an angle to the -axis. In principle, is a self-similar set having overlaps. In this paper we give a complete characterization on which the projection is totally self-similar. We also study the spectrum of , which turns out that the spectrum achieves its maximum value if and only if is totally self-similar. Furthermore, when is totally self-similar, we calculate its Hausdorff dimension and study the subset which consists of all having a unique coding. In particular, we show that for Lebesgue almost every . Finally, for we prove that the possibility for to contain an interval is strictly smaller than that for to have an exact overlap.
{"title":"Projections of four corner Cantor set: Total self-similarity, spectrum and unique codings","authors":"Derong Kong, Beibei Sun","doi":"10.1016/j.indag.2024.08.006","DOIUrl":"https://doi.org/10.1016/j.indag.2024.08.006","url":null,"abstract":"Given , the four corner Cantor set is a self-similar set generated by the iterated function system For let be the orthogonal projection of onto a line with an angle to the -axis. In principle, is a self-similar set having overlaps. In this paper we give a complete characterization on which the projection is totally self-similar. We also study the spectrum of , which turns out that the spectrum achieves its maximum value if and only if is totally self-similar. Furthermore, when is totally self-similar, we calculate its Hausdorff dimension and study the subset which consists of all having a unique coding. In particular, we show that for Lebesgue almost every . Finally, for we prove that the possibility for to contain an interval is strictly smaller than that for to have an exact overlap.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180748","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 : 2024-09-02DOI: 10.1016/j.indag.2024.08.003
Claudio Pedrini
Let be a smooth cubic fourfold. A well known conjecture asserts that is rational if and only if there a Hodge theoretically associated K3 surface . The surface can be associated to in two other different ways. If there is an equivalence of categories where is the Kuznetsov component of and is a Brauer class, or if there is an isomorphism between the transcendental motive and the (twisted ) transcendental motive of a K3 surface . In this note we consider families of cubic fourfolds with a finite group of automorphisms and describe the cases where there is an associated K3 surface in one of the above senses.
{"title":"K3 surfaces associated to a cubic fourfold","authors":"Claudio Pedrini","doi":"10.1016/j.indag.2024.08.003","DOIUrl":"https://doi.org/10.1016/j.indag.2024.08.003","url":null,"abstract":"Let be a smooth cubic fourfold. A well known conjecture asserts that is rational if and only if there a Hodge theoretically associated K3 surface . The surface can be associated to in two other different ways. If there is an equivalence of categories where is the Kuznetsov component of and is a Brauer class, or if there is an isomorphism between the transcendental motive and the (twisted ) transcendental motive of a K3 surface . In this note we consider families of cubic fourfolds with a finite group of automorphisms and describe the cases where there is an associated K3 surface in one of the above senses.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"50 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142248891","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}
{"title":"Enveloping balls of Szlenk derivations","authors":"Tomasz Kochanek, Marek Miarka","doi":"10.1016/j.indag.2024.08.007","DOIUrl":"https://doi.org/10.1016/j.indag.2024.08.007","url":null,"abstract":"For Banach spaces with a shrinking FDD, we provide estimates for the radii of the enveloping balls of the -Szlenk derivations of the dual unit ball.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180794","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 : 2024-08-30DOI: 10.1016/j.indag.2024.08.005
J.W. Bober, L. Du, D. Fretwell, G.S. Kopp, T.D. Wooley
We investigate -superirreducible polynomials, by which we mean irreducible polynomials that remain irreducible under any polynomial substitution of positive degree at most . Let be a finite field of characteristic . We show that no 2-superirreducible polynomials exist in when and that no such polynomials of odd degree exist when is odd. We address the remaining case in which is odd and the polynomials have even degree by giving an explicit formula for the number of monic 2-superirreducible polynomials having even degree . This formula is analogous to that given by Gauss for the number of monic irreducible polynomials of given degree over a finite field. We discuss the associated asymptotic behaviour when either the degree of the polynomial or the size of the finite field tends to infinity.
{"title":"On 2-superirreducible polynomials over finite fields","authors":"J.W. Bober, L. Du, D. Fretwell, G.S. Kopp, T.D. Wooley","doi":"10.1016/j.indag.2024.08.005","DOIUrl":"https://doi.org/10.1016/j.indag.2024.08.005","url":null,"abstract":"We investigate -superirreducible polynomials, by which we mean irreducible polynomials that remain irreducible under any polynomial substitution of positive degree at most . Let be a finite field of characteristic . We show that no 2-superirreducible polynomials exist in when and that no such polynomials of odd degree exist when is odd. We address the remaining case in which is odd and the polynomials have even degree by giving an explicit formula for the number of monic 2-superirreducible polynomials having even degree . This formula is analogous to that given by Gauss for the number of monic irreducible polynomials of given degree over a finite field. We discuss the associated asymptotic behaviour when either the degree of the polynomial or the size of the finite field tends to infinity.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180749","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 : 2024-08-30DOI: 10.1016/j.indag.2024.08.004
Minyoung Jeon
We establish combinatorial and inductive formulas for Kazhdan–Lusztig polynomials associated to covexillary elements in classical types, extending results of Boe, Lascoux–Schützenberger, Sankaran–Vanchinathan, and Zelevinsky for Grassmannians of classical types. The proof uses intersection cohomology theory and the isomorphism of Kazhdan–Lusztig varieties from Anderson–Ikeda–Jeon–Kawago.
{"title":"Covexillary Schubert varieties and Kazhdan–Lusztig polynomials","authors":"Minyoung Jeon","doi":"10.1016/j.indag.2024.08.004","DOIUrl":"https://doi.org/10.1016/j.indag.2024.08.004","url":null,"abstract":"We establish combinatorial and inductive formulas for Kazhdan–Lusztig polynomials associated to covexillary elements in classical types, extending results of Boe, Lascoux–Schützenberger, Sankaran–Vanchinathan, and Zelevinsky for Grassmannians of classical types. The proof uses intersection cohomology theory and the isomorphism of Kazhdan–Lusztig varieties from Anderson–Ikeda–Jeon–Kawago.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180750","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 : 2024-08-20DOI: 10.1016/j.indag.2024.08.002
D. Maksimova
We improve on Gonek–Montgomery’s quantitative version of Kronecker’s approximation theorem.
我们改进了戈内克-蒙哥马利对克罗内克近似定理的量化版本。
{"title":"A note on Kronecker’s approximation theorem","authors":"D. Maksimova","doi":"10.1016/j.indag.2024.08.002","DOIUrl":"https://doi.org/10.1016/j.indag.2024.08.002","url":null,"abstract":"We improve on Gonek–Montgomery’s quantitative version of Kronecker’s approximation theorem.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"80 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180751","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 : 2024-08-17DOI: 10.1016/j.indag.2024.08.001
Manish Kumar Pandey, Lalit Vaishya
In the article, we consider a question concerning the estimation of summatory function of the Fourier coefficients of Hecke eigenforms indexed by a sparse set of integers. In particular, we provide an estimate for the following sum; where means that sum runs over the square-free positive integers, denotes the normalised th Fourier coefficients of a Hecke eigenform of integral weight for the congruence subgroup and is a primitive integral positive-definite binary quadratic forms of fixed discriminant with the class number . As a consequence, we determine the size, in terms of conductor of associated -function, for the first sign change of Hecke eigenvalues indexed by the integers which are represented by . This work is an improvement and generalisation of the previous results.
{"title":"First moment of Hecke eigenvalues at the integers represented by binary quadratic forms","authors":"Manish Kumar Pandey, Lalit Vaishya","doi":"10.1016/j.indag.2024.08.001","DOIUrl":"https://doi.org/10.1016/j.indag.2024.08.001","url":null,"abstract":"In the article, we consider a question concerning the estimation of summatory function of the Fourier coefficients of Hecke eigenforms indexed by a sparse set of integers. In particular, we provide an estimate for the following sum; where means that sum runs over the square-free positive integers, denotes the normalised th Fourier coefficients of a Hecke eigenform of integral weight for the congruence subgroup and is a primitive integral positive-definite binary quadratic forms of fixed discriminant with the class number . As a consequence, we determine the size, in terms of conductor of associated -function, for the first sign change of Hecke eigenvalues indexed by the integers which are represented by . This work is an improvement and generalisation of the previous results.","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"29 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180791","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 : 2024-07-01DOI: 10.1016/j.indag.2024.07.010
Ben Moonen
{"title":"A remark on the paper of Deninger and Murre","authors":"Ben Moonen","doi":"10.1016/j.indag.2024.07.010","DOIUrl":"https://doi.org/10.1016/j.indag.2024.07.010","url":null,"abstract":"","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"17 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141844337","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 : 2024-06-01DOI: 10.1016/j.indag.2024.05.007
Christopher Deninger
{"title":"Dynamical systems for arithmetic schemes","authors":"Christopher Deninger","doi":"10.1016/j.indag.2024.05.007","DOIUrl":"https://doi.org/10.1016/j.indag.2024.05.007","url":null,"abstract":"","PeriodicalId":501252,"journal":{"name":"Indagationes Mathematicae","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141513686","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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