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Journal d'Analyse Mathématique最新文献

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Bloch varieties and quantum ergodicity for periodic graph operators 周期图算子的布洛赫变种和量子遍历性
Journal d'Analyse Mathématique Pub Date : 2024-09-12 DOI: 10.1007/s11854-024-0339-y
Wencai Liu
{"title":"Bloch varieties and quantum ergodicity for periodic graph operators","authors":"Wencai Liu","doi":"10.1007/s11854-024-0339-y","DOIUrl":"https://doi.org/10.1007/s11854-024-0339-y","url":null,"abstract":"<p>For periodic graph operators, we establish criteria to determine the overlaps of spectral band functions based on Bloch varieties. One criterion states that for a large family of periodic graph operators, the irreducibility of Bloch varieties implies no non-trivial periods for spectral band functions. This particularly shows that spectral band functions of discrete periodic Schrödinger operators on ℤ<sup><i>d</i></sup> have no non-trivial periods, answering positively a question asked by Mckenzie and Sabri [Quantum ergodicity for periodic graphs, Comm. Math. Phys. 403 (2023), 1477–1509].</p>","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142266660","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}
引用次数: 0
On the Central Limit Theorem for linear eigenvalue statistics on random surfaces of large genus 论大属随机曲面上线性特征值统计的中心极限定理
Journal d'Analyse Mathématique Pub Date : 2023-12-22 DOI: 10.1007/s11854-023-0327-7
Zeév Rudnick, Igor Wigman
{"title":"On the Central Limit Theorem for linear eigenvalue statistics on random surfaces of large genus","authors":"Zeév Rudnick, Igor Wigman","doi":"10.1007/s11854-023-0327-7","DOIUrl":"https://doi.org/10.1007/s11854-023-0327-7","url":null,"abstract":"<p>We study the fluctuations of smooth linear statistics of Laplace eigenvalues of compact hyperbolic surfaces lying in short energy windows, when averaged over the moduli space of surfaces of a given genus. The average is taken with respect to the Weil–Petersson measure. We show that first taking the large genus limit, then a short window limit, the distribution tends to a Gaussian. The variance was recently shown to be given by the corresponding quantity for the Gaussian Orthogonal Ensemble (GOE), and the Gaussian fluctuations are also consistent with those in Random Matrix Theory, as conjectured in the physics literature for a fixed surface.</p>","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139023918","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}
引用次数: 0
Stability and instability of lattices in semisimple groups 半简单群中网格的稳定性和不稳定性
Journal d'Analyse Mathématique Pub Date : 2023-12-22 DOI: 10.1007/s11854-023-0329-5
Uri Bader, Alexander Lubotzky, Roman Sauer, Shmuel Weinberger
{"title":"Stability and instability of lattices in semisimple groups","authors":"Uri Bader, Alexander Lubotzky, Roman Sauer, Shmuel Weinberger","doi":"10.1007/s11854-023-0329-5","DOIUrl":"https://doi.org/10.1007/s11854-023-0329-5","url":null,"abstract":"<p>Using cohomological methods, we show that lattices in semisimple groups are typically stable with respect to the Frobenius norm but not with respect to the operator norm.</p>","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139025423","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}
引用次数: 0
Bounds for theta sums in higher rank. II 高阶θ 和的边界。二
Journal d'Analyse Mathématique Pub Date : 2023-12-22 DOI: 10.1007/s11854-023-0333-9
Jens Marklof, Matthew Welsh
{"title":"Bounds for theta sums in higher rank. II","authors":"Jens Marklof, Matthew Welsh","doi":"10.1007/s11854-023-0333-9","DOIUrl":"https://doi.org/10.1007/s11854-023-0333-9","url":null,"abstract":"<p>In the first paper of this series we established new upper bounds for multi-variable exponential sums associated with a quadratic form. The present study shows that if one adds a linear term in the exponent, the estimates can be further improved for almost all parameter values. Our results extend the bound for one-variable theta sums obtained by Fedotov and Klopp in 2012.</p>","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886401","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}
引用次数: 0
The unipotent mixing conjecture 单能混合猜想
Journal d'Analyse Mathématique Pub Date : 2023-12-22 DOI: 10.1007/s11854-023-0326-8
Valentin Blomer, Philippe Michel
{"title":"The unipotent mixing conjecture","authors":"Valentin Blomer, Philippe Michel","doi":"10.1007/s11854-023-0326-8","DOIUrl":"https://doi.org/10.1007/s11854-023-0326-8","url":null,"abstract":"<p>We show that shifted pairs of discrete or continuous low-lying horocycles equidistribute in the product space of two modular curves.</p>","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886600","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}
引用次数: 0
Determinants of Laplacians on random hyperbolic surfaces 随机双曲面上拉普拉斯的确定性
Journal d'Analyse Mathématique Pub Date : 2023-12-22 DOI: 10.1007/s11854-023-0334-8
Frédéric Naud
{"title":"Determinants of Laplacians on random hyperbolic surfaces","authors":"Frédéric Naud","doi":"10.1007/s11854-023-0334-8","DOIUrl":"https://doi.org/10.1007/s11854-023-0334-8","url":null,"abstract":"<p>For sequences (<i>X</i><sub><i>j</i></sub>) of random closed hyperbolic surfaces with volume Vol(<i>X</i><sub><i>j</i></sub>) tending to infinity, we prove that there exists a universal constant <i>E</i> &gt; 0 such that for all <i>ϵ</i> &gt; 0, the regularized determinant of the Laplacian satisfies </p><span>$${{log det ({Delta _{{X_j}}})} over {{rm{Vol}}({X_j})}} in [E -epsilon ,E +epsilon]$$</span><p> with high probability as <i>j</i> → +⋡. This result holds for various models of random surfaces, including the Weil–Petersson model.</p>","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"87 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030317","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}
引用次数: 0
Quantitative equidistribution and the local statistics of the spectrum of a flat torus 平环面频谱的定量等分布和局部统计
Journal d'Analyse Mathématique Pub Date : 2023-12-22 DOI: 10.1007/s11854-023-0332-x
Elon Lindenstrauss, Amir Mohammadi, Zhiren Wang
{"title":"Quantitative equidistribution and the local statistics of the spectrum of a flat torus","authors":"Elon Lindenstrauss, Amir Mohammadi, Zhiren Wang","doi":"10.1007/s11854-023-0332-x","DOIUrl":"https://doi.org/10.1007/s11854-023-0332-x","url":null,"abstract":"<p>We show that a pair correlation function for the spectrum of a flat 2-dimensional torus satisfying an explicit Diophantine condition agrees with those of a Poisson process with a polynomial error rate.</p><p>The proof is based on a quantitative equidistribution theorem and tools from geometry of numbers.</p>","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886370","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}
引用次数: 0
Central limit theorems for random multiplicative functions 随机乘法函数的中心极限定理
Journal d'Analyse Mathématique Pub Date : 2023-12-22 DOI: 10.1007/s11854-023-0331-y
Kannan Soundararajan, Max Wenqiang Xu
{"title":"Central limit theorems for random multiplicative functions","authors":"Kannan Soundararajan, Max Wenqiang Xu","doi":"10.1007/s11854-023-0331-y","DOIUrl":"https://doi.org/10.1007/s11854-023-0331-y","url":null,"abstract":"<p>A Steinhaus random multiplicative function <i>f</i> is a completely multiplicative function obtained by setting its values on primes <i>f</i>(<i>p</i>) to be independent random variables distributed uniformly on the unit circle. Recent work of Harper shows that <span>(sumnolimits_{n le N} {f(n)} )</span> exhibits “more than square-root cancellation,” and in particular <span>({1 over {sqrt N }}sumnolimits_{n le N} {f(n)} )</span> does not have a (complex) Gaussian distribution. This paper studies <span>(sumnolimits_{n in {cal A}} {f(n)} )</span>, where <span>({cal A})</span> is a subset of the integers in [1, <i>N</i>], and produces several new examples of sets <span>({cal A})</span> where a central limit theorem can be established. We also consider more general sums such as <span>(sumnolimits_{n le N} {f(n){e^{2pi intheta }}} )</span>, where we show that a central limit theorem holds for any irrational <i>θ</i> that does not have extremely good Diophantine approximations.</p>","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886267","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}
引用次数: 0
On the analytic theory of isotropic ternary quadratic forms 论各向同性三元二次型的解析理论
Journal d'Analyse Mathématique Pub Date : 2023-12-22 DOI: 10.1007/s11854-023-0324-x
William Duke, Rainer Schulze-Pillot
{"title":"On the analytic theory of isotropic ternary quadratic forms","authors":"William Duke, Rainer Schulze-Pillot","doi":"10.1007/s11854-023-0324-x","DOIUrl":"https://doi.org/10.1007/s11854-023-0324-x","url":null,"abstract":"<p>A new local-global result about the primitive representations of zero by integral ternary quadratic forms is proven. By an extension of a result of Kneser (given in the Appendix), it yields a quantitative supplement to the Hasse principle on the number of automorphic orbits of primitive zeros of a genus of forms. One ingredient in its proof is an asymptotic formula for a count of the zeros of a given form in such an orbit.</p>","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139030461","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}
引用次数: 0
Smooth numbers and the Dickman ρ function 平滑数和迪克曼 ρ 函数
Journal d'Analyse Mathématique Pub Date : 2023-12-22 DOI: 10.1007/s11854-023-0328-6
Ofir Gorodetsky
{"title":"Smooth numbers and the Dickman ρ function","authors":"Ofir Gorodetsky","doi":"10.1007/s11854-023-0328-6","DOIUrl":"https://doi.org/10.1007/s11854-023-0328-6","url":null,"abstract":"<p>We establish an asymptotic formula for ψ(<i>x, y</i>) whose shape is <i>xρ</i>(log <i>x</i>/ log <i>y</i>) times correction factors. These factors take into account the contributions of zeta zeros and prime powers and the formula can be regarded as an (approximate) explicit formula for ψ(<i>x, y</i>). With this formula at hand we prove oscillation results for ψ(<i>x, y</i>), which resolve a question of Hildebrand on the range of validity of ψ(<i>x, y</i>) ≍ <i>xρ</i>(log <i>x</i>/ log <i>y</i>). We also address a question of Pomerance on the range of validity of ψ(<i>x, y</i>) ≥ <i>xρ</i>(log <i>x/</i> log <i>y</i>).</p><p>Along the way we improve classical estimates for ψ(<i>x, y</i>) and, on the Riemann Hypothesis, uncover an unexpected phase transition of ψ(<i>x, y</i>)at <i>y</i> = (log <i>x</i>)<sup>3/2+<i>o</i>(1)</sup>.</p>","PeriodicalId":502135,"journal":{"name":"Journal d'Analyse Mathématique","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886265","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}
引用次数: 0
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