Indagationes Mathematicae-New Series最新文献

{"title":"Relatively prime pairs in the Piatetski-Shapiro sequences","authors":"Yuta Suzuki","doi":"10.1016/j.indag.2025.08.001","DOIUrl":"10.1016/j.indag.2025.08.001","url":null,"abstract":"<div><div>In this paper, we prove an asymptotic formula for the number of relatively prime pairs in the Piatetski-Shapiro sequence of arbitrarily large order. This result improves the result of Pimsert et al. (2023), the order of which was restricted to be <span><math><mrow><mo>&lt;</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></math></span>. The key ingredients of the proof are a simple averaging trick and an extension of Deshouillers’ result on the distribution of the Piatetski-Shapiro sequence in arithmetic progressions.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1148-1157"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148539553","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two notes on Spin(7)-structures","authors":"Kamil Niedziałomski","doi":"10.1016/j.indag.2025.09.007","DOIUrl":"10.1016/j.indag.2025.09.007","url":null,"abstract":"<div><div>We derive the explicit formula for the intrinsic torsion of a Spin(7)-structure on an 8-dimensional Riemannian manifold <span><math><mi>M</mi></math></span>. Here, the intrinsic torsion is a difference of the minimal Spin(7)-connection and the Levi-Civita connection. The formula relates the intrinsic torsion with the Lee form <span><math><mi>θ</mi></math></span> and <span><math><msubsup><mrow><mi>Λ</mi></mrow><mrow><mn>48</mn></mrow><mrow><mn>3</mn></mrow></msubsup></math></span>-component <span><math><msub><mrow><mrow><mo>(</mo><mi>δ</mi><mi>Φ</mi><mo>)</mo></mrow></mrow><mrow><mn>48</mn></mrow></msub></math></span> of a codifferential <span><math><mrow><mi>δ</mi><mi>Φ</mi></mrow></math></span> of the 4-form defining a given structure. Using the formula obtained, we compute the condition for a Spin(7) structure of type <span><math><msub><mrow><mi>W</mi></mrow><mrow><mn>8</mn></mrow></msub></math></span> to be (second order) nearly parallel. Moreover, applying the divergence formula obtained by the author for general Riemannian <span><math><mi>G</mi></math></span>-structure in another article, we rediscover the well known formula for the scalar curvature in terms of norms of <span><math><mi>θ</mi></math></span>, <span><math><msub><mrow><mrow><mo>(</mo><mi>δ</mi><mi>Φ</mi><mo>)</mo></mrow></mrow><mrow><mn>48</mn></mrow></msub></math></span> and the divergence <span><math><mrow><mi>div</mi><mi>θ</mi></mrow></math></span>. We justify the formula on appropriate examples.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1306-1321"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Simpliciality of vector-valued function spaces","authors":"Ondřej F.K. Kalenda,&nbsp;Jiří Spurný","doi":"10.1016/j.indag.2025.10.002","DOIUrl":"10.1016/j.indag.2025.10.002","url":null,"abstract":"<div><div>We investigate integral representation of vector-valued function spaces, i.e., of subspaces <span><math><mrow><mi>H</mi><mo>⊂</mo><mi>C</mi><mrow><mo>(</mo><mi>K</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></mrow></math></span>, where <span><math><mi>K</mi></math></span> is a compact space and <span><math><mi>E</mi></math></span> is a (real or complex) Banach space. We point out that there are two possible ways of generalizing representation theorems known from the scalar case — either one may represent (all) functionals from <span><math><msup><mrow><mi>H</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> using <span><math><msup><mrow><mi>E</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span>-valued vector measures on <span><math><mi>K</mi></math></span> (as it is done in the literature) or one may represent (some) operators from <span><math><mrow><mi>L</mi><mrow><mo>(</mo><mi>H</mi><mo>,</mo><mi>E</mi><mo>)</mo></mrow></mrow></math></span> by scalar measures on <span><math><mi>K</mi></math></span> using the Bochner integral. These two ways lead to two different notions of simpliciality which we call ‘vector simpliciality’ and ‘weak simpliciality’. It turns out that these two notions are in general incomparable. Moreover, the weak simpliciality is not affected by renorming the target space <span><math><mi>E</mi></math></span>, while vector simpliciality may be affected. Further, if <span><math><mi>H</mi></math></span> contains constants, vector simpliciality is strictly stronger and admits several characterizations (partially analogous to the characterizations known in the scalar case). We also study orderings of measures inspired by C.J.K. Batty which may be (in special cases) used to characterize <span><math><mi>H</mi></math></span>-boundary measures. Finally, we give a finer version of representation theorem using positive measures on <span><math><mrow><mi>K</mi><mo>×</mo><msub><mrow><mi>B</mi></mrow><mrow><msup><mrow><mi>E</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></msub></mrow></math></span> and characterize uniqueness in this case.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1362-1430"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ratios conjecture of cubic L-functions of prime moduli","authors":"Peng Gao,&nbsp;Liangyi Zhao","doi":"10.1016/j.indag.2025.07.001","DOIUrl":"10.1016/j.indag.2025.07.001","url":null,"abstract":"<div><div>We develop <span><math><mi>L</mi></math></span>-functions ratios conjecture with one shift in the numerator and denominator in certain ranges for the family of cubic Hecke <span><math><mi>L</mi></math></span>-functions of prime moduli over the Eisenstein field using multiple Dirichlet series under the generalized Riemann hypothesis. As applications, we evaluate asymptotically the first moment of central values as well as the one-level density of the same family of <span><math><mi>L</mi></math></span>-functions.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1065-1083"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bounds for moments of quadratic Dirichlet character sums of prime moduli","authors":"Yuetong Zhao","doi":"10.1016/j.indag.2025.11.003","DOIUrl":"10.1016/j.indag.2025.11.003","url":null,"abstract":"<div><div>Assuming the generalized Riemann hypothesis, we evaluate sharp upper bounds for the shifted moments of quadratic Dirichlet <span><math><mi>L</mi></math></span>-functions with moduli 8<span><math><mi>p</mi></math></span>, where <span><math><mi>p</mi></math></span> ranges over odd primes. We then apply this result to prove bounds for the moments of quadratic Dirichlet character sums with prime moduli.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1557-1585"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148542039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modulation spaces on the Heisenberg group","authors":"Md Hasan Ali Biswas,&nbsp;Sundaram Thangavelu","doi":"10.1016/j.indag.2025.09.002","DOIUrl":"10.1016/j.indag.2025.09.002","url":null,"abstract":"<div><div>In this article we show how certain irreducible unitary representation <span><math><msub><mrow><mi>Π</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> of the twisted Heisenberg group <span><math><mrow><msubsup><mrow><mi>H</mi></mrow><mrow><mi>λ</mi></mrow><mrow><mi>n</mi></mrow></msubsup><mrow><mo>(</mo><mi>ℂ</mi><mo>)</mo></mrow></mrow></math></span> leads to the twisted modulation spaces <span><math><mrow><msubsup><mrow><mi>M</mi></mrow><mrow><mi>λ</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msubsup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msup><mo>)</mo></mrow><mo>.</mo></mrow></math></span> These <span><math><msub><mrow><mi>Π</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> also turn out to be irreducible unitary representations of another nilpotent Lie group <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> which contains two copies of the Heisenberg group <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>.</mo></mrow></math></span> By lifting <span><math><msub><mrow><mi>Π</mi></mrow><mrow><mi>λ</mi></mrow></msub></math></span> we obtain another unitary representation <span><math><mi>Π</mi></math></span> of <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> acting on <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow><mo>.</mo></mrow></math></span> We define our modulation spaces <span><math><mrow><msup><mrow><mi>M</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> in terms of the matrix coefficients associated to <span><math><mrow><mi>Π</mi><mo>.</mo></mrow></math></span> These spaces are shown to be invariant under Heisenberg translations and Heisenberg modulations which are different from euclidean modulations. We also establish some of the basic properties of <span><math><mrow><msubsup><mrow><mi>M</mi></mrow><mrow><mi>λ</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msubsup><mrow><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><msup><mrow><mi>M</mi></mrow><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></msup><mrow><mo>(</mo><msup><mrow><mi>H</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> such as completeness and invariance under suitable Fourier transforms.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1250-1279"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546655","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Non-repetition of second coefficients of Hecke polynomials","authors":"Archer Clayton,&nbsp;Helen Dai,&nbsp;Tianyu Ni,&nbsp;Erick Ross,&nbsp;Hui Xue,&nbsp;Jake Zummo","doi":"10.1016/j.indag.2025.07.009","DOIUrl":"10.1016/j.indag.2025.07.009","url":null,"abstract":"<div><div>Let <span><math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mn>2</mn><mi>k</mi><mo>)</mo></mrow></mrow></math></span> denote the <span><math><mi>m</mi></math></span>th Hecke operator on the space <span><math><mrow><msub><mrow><mi>S</mi></mrow><mrow><mn>2</mn><mi>k</mi></mrow></msub><mrow><mo>(</mo><msub><mrow><mi>Γ</mi></mrow><mrow><mn>0</mn></mrow></msub><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow><mo>)</mo></mrow></mrow></math></span> of cuspidal modular forms of weight <span><math><mrow><mn>2</mn><mi>k</mi></mrow></math></span> and level <span><math><mi>N</mi></math></span>. In this paper, we study the non-repetition of the second coefficient of the characteristic polynomial of <span><math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>m</mi></mrow></msub><mrow><mo>(</mo><mi>N</mi><mo>,</mo><mn>2</mn><mi>k</mi><mo>)</mo></mrow></mrow></math></span>. We obtain results in the horizontal aspect (where <span><math><mi>m</mi></math></span> varies), the vertical aspect (where <span><math><mi>k</mi></math></span> varies), and the level aspect (where <span><math><mi>N</mi></math></span> varies). Finally, we use these non-repetition results to extend a result of Vilardi and Xue on distinguishing Hecke eigenforms.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1117-1135"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546610","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Archimedean vector lattice functional calculus for semicontinuous positively homogeneous functions","authors":"C. Schwanke","doi":"10.1016/j.indag.2025.11.002","DOIUrl":"10.1016/j.indag.2025.11.002","url":null,"abstract":"<div><div>We develop a functional calculus on Archimedean vector lattices for semicontinuous positively homogeneous real-valued functions defined on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> which are bounded on the unit sphere. This functional calculus is constructed independently of other functional calculi in the literature, although we show after its establishment that it agrees with the Borel positively homogeneous functional calculus on Dedekind <span><math><mi>σ</mi></math></span>-complete vector lattices. Furthermore, and perhaps most significantly, it provides concrete formulas, for a wide class of functions abstractly defined via functional calculus, which are completely in terms of vector lattice operations. Finally, we provide some examples to illustrate the utility of the theory presented.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1524-1556"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Failure of orthogonality of rounded Fourier bases","authors":"François Clément,&nbsp;Stefan Steinerberger","doi":"10.1016/j.indag.2025.07.010","DOIUrl":"10.1016/j.indag.2025.07.010","url":null,"abstract":"<div><div>The purpose of this note is to report a curious phenomenon when replacing the entries of an (orthogonal) Fourier matrix by their sign (which, generically, will destroy orthogonality of the matrix). We prove estimates for the inner product between two rows, that is <span><span><span><math><mrow><mrow><mo>|</mo><munderover><mrow><mo>∑</mo></mrow><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></munderover><mo>sign</mo><mfenced><mrow><mo>cos</mo><mfenced><mrow><mfrac><mrow><mn>2</mn><mi>π</mi><mi>a</mi></mrow><mrow><mi>n</mi></mrow></mfrac><mi>k</mi></mrow></mfenced></mrow></mfenced><mo>sign</mo><mfenced><mrow><mo>cos</mo><mfenced><mrow><mfrac><mrow><mn>2</mn><mi>π</mi><mi>b</mi></mrow><mrow><mi>n</mi></mrow></mfrac><mi>k</mi></mrow></mfenced></mrow></mfenced><mo>|</mo></mrow><mo>,</mo></mrow></math></span></span></span>when <span><math><mi>n</mi></math></span> is prime and <span><math><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>∈</mo><mi>N</mi></mrow></math></span>. We show that the expression can only be large if <span><math><mrow><msup><mrow><mi>a</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mi>b</mi><mo>∈</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span> (or a small multiple thereof) is close to 1. This explains some of the surprising line patterns in <span><math><mrow><msup><mrow><mi>A</mi></mrow><mrow><mi>T</mi></mrow></msup><mi>A</mi></mrow></math></span> when <span><math><mrow><mi>A</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></msup></mrow></math></span> is the signed discrete cosine transform. Similar results seem to exist at a great level of generality.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1136-1147"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A characterization of Kazhdan–Lusztig right cells containing smooth elements","authors":"Zhanqiang Bai,&nbsp;Zheng-An Chen","doi":"10.1016/j.indag.2025.10.001","DOIUrl":"10.1016/j.indag.2025.10.001","url":null,"abstract":"<div><div>Let <span><math><mi>g</mi></math></span> be the Lie algebra <span><math><mrow><mi>sl</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>ℂ</mi><mo>)</mo></mrow></mrow></math></span>. Its Weyl group is the symmetric group <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>. In this paper, we want to describe some Kazhdan–Lusztig right cells containing smooth elements which parameterize the smooth Schubert varieties. These elements are closely related to the study of associated varieties of highest weight modules of <span><math><mrow><mi>sl</mi><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>ℂ</mi><mo>)</mo></mrow></mrow></math></span>. Firstly, we give a complete classification of the KL right cells containing only smooth elements. Then we give a sufficient condition for a KL right cell to contain only non-smooth elements by using invariant subsequences and a sufficient condition for a KL right cell to contain some smooth elements. Finally, we give an efficient algorithm to find out all the smooth elements in a given KL right cell.</div></div>","PeriodicalId":56126,"journal":{"name":"Indagationes Mathematicae-New Series","volume":"37 4","pages":"Pages 1341-1361"},"PeriodicalIF":0.8,"publicationDate":"2026-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148546617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}