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Endpoint $ell^r$ improving estimates for prime averages 端点$ well ^r$改善素数平均值的估计
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-25 DOI: 10.4310/mrl.2022.v29.n6.a6
M. Lacey, H. Mousavi, Yaghoub Rahimi
{"title":"Endpoint $ell^r$ improving estimates for prime averages","authors":"M. Lacey, H. Mousavi, Yaghoub Rahimi","doi":"10.4310/mrl.2022.v29.n6.a6","DOIUrl":"https://doi.org/10.4310/mrl.2022.v29.n6.a6","url":null,"abstract":"Let $ Lambda $ denote von Mangoldt's function, and consider the averages begin{align*} A_N f (x)&=frac{1}{N}sum_{1leq n leq N}f(x-n)Lambda(n) . end{align*} We prove sharp $ ell ^{p}$-improving for these averages, and sparse bounds for the maximal function. The simplest inequality is that for sets $ F, Gsubset [0,N]$ there holds begin{equation*} N ^{-1} langle A_N mathbf 1_{F} , mathbf 1_{G} rangle ll frac{lvert Frvert cdot lvert Grvert} { N ^2 } Bigl( operatorname {Log} frac{lvert Frvert cdot lvert Grvert} { N ^2 } Bigr) ^{t}, end{equation*} where $ t=2$, or assuming the Generalized Riemann Hypothesis, $ t=1$. The corresponding sparse bound is proved for the maximal function $ sup_N A_N mathbf 1_{F}$. The inequalities for $ t=1$ are sharp. The proof depends upon the Circle Method, and an interpolation argument of Bourgain.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43964086","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}
引用次数: 2
Automorphisms of products of toric varieties 环缘品种乘积的自同构
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-10 DOI: 10.4310/MRL.2022.v29.n2.a9
Alvaro Liendo, G. Arteche
{"title":"Automorphisms of products of toric varieties","authors":"Alvaro Liendo, G. Arteche","doi":"10.4310/MRL.2022.v29.n2.a9","DOIUrl":"https://doi.org/10.4310/MRL.2022.v29.n2.a9","url":null,"abstract":"A BSTRACT . We give an explicit description of the automorphism group of a product of complete toric varieties over an arbitrary field in terms of the respective automorphism groups of its components. More precisely, we prove that, up to permutation of isomorphic components, an automorphism of a product corresponds to a product of automorphisms of its components. We also reprove, in modern language, the classic result by Demazure describing the group-scheme of automorphisms of a complete toric variety over an arbitrary field.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43031033","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}
引用次数: 5
Einstein manifolds, self-dual Weyl curvature, and conformally Kähler geometry 爱因斯坦流形，自对偶Weyl曲率，和共形Kähler几何
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-01 DOI: 10.4310/MRL.2021.V28.N1.A6
C. LeBrun
{"title":"Einstein manifolds, self-dual Weyl curvature, and conformally Kähler geometry","authors":"C. LeBrun","doi":"10.4310/MRL.2021.V28.N1.A6","DOIUrl":"https://doi.org/10.4310/MRL.2021.V28.N1.A6","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70517073","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}
引用次数: 5
Commutative subalgebras of $mathcal{U}(mathfrak{q})$ of maximal transcendence degree 最大超越度$mathcal{U}(mathfrak{q})$的交换子代数
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-01 DOI: 10.4310/MRL.2021.V28.N3.A12
O. Yakimova
{"title":"Commutative subalgebras of $mathcal{U}(mathfrak{q})$ of maximal transcendence degree","authors":"O. Yakimova","doi":"10.4310/MRL.2021.V28.N3.A12","DOIUrl":"https://doi.org/10.4310/MRL.2021.V28.N3.A12","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516687","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}
引用次数: 0
$4d$ $N=2$ SCFT and singularity theory Part IV: Isolated rational Gorenstein non-complete intersection singularities with at least one-dimensional deformation and nontrivial $T^2$ $4d$ N=2$ SCFT与奇点理论第四部分:具有至少一维变形和非平凡$T^2$的孤立有理Gorenstein非完全相交奇点
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-01 DOI: 10.4310/MRL.2021.V28.N1.A1
Bingyi Chen, S. Yau, S. Yau, Huaiqing Zuo
{"title":"$4d$ $N=2$ SCFT and singularity theory Part IV: Isolated rational Gorenstein non-complete intersection singularities with at least one-dimensional deformation and nontrivial $T^2$","authors":"Bingyi Chen, S. Yau, S. Yau, Huaiqing Zuo","doi":"10.4310/MRL.2021.V28.N1.A1","DOIUrl":"https://doi.org/10.4310/MRL.2021.V28.N1.A1","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516435","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}
引用次数: 1
Slope filtrations of $F$-isocrystals and logarithmic decay $F$-等晶的斜率过滤和对数衰减
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-01 DOI: 10.4310/MRL.2021.V28.N1.A5
Joe Kramer-Miller
{"title":"Slope filtrations of $F$-isocrystals and logarithmic decay","authors":"Joe Kramer-Miller","doi":"10.4310/MRL.2021.V28.N1.A5","DOIUrl":"https://doi.org/10.4310/MRL.2021.V28.N1.A5","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516498","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}
引用次数: 2
On the existence of specialization isomorphisms of admissible fundamental groups in positive characteristic 论正特征上可容许基群的专门化同构的存在性
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-01 DOI: 10.4310/mrl.2021.v28.n6.a11
Yu Yang
{"title":"On the existence of specialization isomorphisms of admissible fundamental groups in positive characteristic","authors":"Yu Yang","doi":"10.4310/mrl.2021.v28.n6.a11","DOIUrl":"https://doi.org/10.4310/mrl.2021.v28.n6.a11","url":null,"abstract":"Let p be a prime number, and let Mg,n be the moduli stack over an algebraic closure Fp of the finite field Fp parameterizing pointed stable curves of type (g, n), Mg,n the open substack of Mg,n parameterizing smooth pointed stable curves, Mg,n the coarse moduli space of Mg,n, Mg,n the coarse moduli space of Mg,n, q ∈ Mg,n an arbitrary point, and Πq the admissible fundamental group of a pointed stable curve corresponding to a geometric point over q. In the present paper, we prove that, there exists q1, q2 ∈ Mg,n Mg,n such that q1 is a specialization of q2, that q1 ̸= q2, and that a specialization homomorphism sp : Πq2 ↠ Πq1 is an isomorphism.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516919","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}
引用次数: 4
Gottschalk–Hedlund theorem revisited 重新审视戈特沙尔克-赫德隆德定理
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-01 DOI: 10.4310/MRL.2021.V28.N1.A12
Xifeng Su, P. Thieullen
{"title":"Gottschalk–Hedlund theorem revisited","authors":"Xifeng Su, P. Thieullen","doi":"10.4310/MRL.2021.V28.N1.A12","DOIUrl":"https://doi.org/10.4310/MRL.2021.V28.N1.A12","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516449","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}
引用次数: 1
Hörmander Fourier multiplier theorems with optimal regularity in bi-parameter Besov spaces Hörmander双参数Besov空间中最优正则性的傅里叶乘数定理
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-01 DOI: 10.4310/mrl.2021.v28.n4.a4
Jiao Chen, Liang Huang, Guozhen Lu
{"title":"Hörmander Fourier multiplier theorems with optimal regularity in bi-parameter Besov spaces","authors":"Jiao Chen, Liang Huang, Guozhen Lu","doi":"10.4310/mrl.2021.v28.n4.a4","DOIUrl":"https://doi.org/10.4310/mrl.2021.v28.n4.a4","url":null,"abstract":"The main aim of this paper to establish a bi-parameter version of a theorem of Baernstein and Sawyer [1] on boundedness of Fourier multipliers on one-parameter Hardy spaces H p ( R n ) which improves an earlier result of Calder´on and Torchinsky [2]. More pre-cisely, we prove the boundedness of the bi-parameter Fourier multiplier operators on the Lebesgue spaces L p ( R n 1 × R n 2 ) (1 < p < ∞ ) and bi-parameter Hardy spaces H p ( R n 1 × R n 2 ) (0 < p ≤ 1) with optimal regularity for the multiplier being in the bi-parameter Besov spaces B ( n 12 , n 22 ) 2 , 1 ( R n 1 × R n 2 ) and B ( s 1 ,s 2 ) 2 ,q ( R n 1 × R n 2 ). The Besov regularity assumption is clearly weaker than the assumption of the Sobolev regularity. Thus our results sharpen the known H¨ormander multiplier theorem for the bi-parameter Fourier multipliers using the Sobolev regularity in the same spirit as Baernstein and Sawyer improved the result of Calder´on and Torchinsky. Our method is differential from the one used by Baernstein and Sawyer in the one-parameter setting. We employ the bi-parameter Littlewood-Paley-Stein theory and atomic decomposition for the bi-parameter Hardy spaces H p ( R n 1 × R n 2 ) (0 < p ≤ 1) to establish our main result (Theorem 1.6). Moreover, the bi-parameter nature involves much more subtlety in our situation where atoms are supported on arbitrary open sets instead of rectangles.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516813","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}
引用次数: 3
The boundary rigidity for holomorphic self-maps of some fibered domains 某些纤维域的全纯自映射的边界刚性
IF 1 3区 数学
Mathematical Research Letters Pub Date : 2021-01-01 DOI: 10.4310/MRL.2021.V28.N3.A4
J. Fornæss, F. Rong
{"title":"The boundary rigidity for holomorphic self-maps of some fibered domains","authors":"J. Fornæss, F. Rong","doi":"10.4310/MRL.2021.V28.N3.A4","DOIUrl":"https://doi.org/10.4310/MRL.2021.V28.N3.A4","url":null,"abstract":"","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70516734","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}
引用次数: 2
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