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Kannan Soundararajan - One of the best experts on this subject based on the ideXlab platform.
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Equidistribution from the Chinese Remainder Theorem
arXiv: Number Theory, 2020Co-Authors: Emmanuel Kowalski, Kannan SoundararajanAbstract:We prove the Equidistribution of subsets of $(\Rr/\Zz)^n$ defined by fractional parts of subsets of~$(\Zz/q\Zz)^n$ that are constructed using the Chinese Remainder Theorem.
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Equidistribution of zeros of polynomials
American Mathematical Monthly, 2019Co-Authors: Kannan SoundararajanAbstract:A classical result of Erdős and Turan states that if a monic polynomial has small size on the unit circle and its constant coefficient is not too small, then its zeros cluster near the unit circle ...
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Equidistribution of zeros of polynomials
arXiv: Classical Analysis and ODEs, 2018Co-Authors: Kannan SoundararajanAbstract:A classical result of Erdos and Turan states that if a monic polynomial has small size on the unit circle and its constant coefficient is not too small, then its zeros cluster near the unit circle and become equidistributed in angle. Using Fourier analysis we give a short and self-contained proof of this result.
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mass Equidistribution for hecke eigenforms
Annals of Mathematics, 2010Co-Authors: Roman Holowinsky, Kannan SoundararajanAbstract:We prove a conjecture of Rudnick and Sarnak on the mass Equidistribution of Hecke eigenforms. This builds upon independent work of the authors.
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mass Equidistribution for hecke eigenforms
arXiv: Number Theory, 2008Co-Authors: Roman Holowinsky, Kannan SoundararajanAbstract:We prove a conjecture of Rudnick and Sarnak on the mass Equidistribution of Hecke eigenforms. This builds upon independent work of the authors see arxiv.org:math/0809.1640 and arxiv.org:math/0809.1635.
Emmanuel Ullmo - One of the best experts on this subject based on the ideXlab platform.
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Equidistribution de sous varietes speciales
Annals of Mathematics, 2005Co-Authors: Laurent Clozel, Emmanuel UllmoAbstract:de points speciaux (les points a multiplication complexe) et un ensemble de sous-varietes speciales que l'on appelle sous-varietes de type de Hodge. Les definitions qui seront donnees plus tard dans le texte sont presentees de maniere tres agreable dans le papier de Moonen [8]. Dans ce cadre Andre et Oort font la conjecture suivante. Soit Y une sousvariete de S, il existe un ensemble fini {S1,..., Sr} de sous-varietes speciales avec Si C Y pour tout i tel que toute variete speciale Z de S contenue dans Y est en fait contenue dans un des Si. Le resultat le plus profond dans la direction de cette conjecture a ete obtenu par Edixhoven et Yafaev [5]. On definit dans ce texte une classe assez large de sous-varietes speciales que nous appellerons fortement speciales par manque d'une terminologie plus adequate. Decrivons les sous-varietes fortement speciales: Soit S une variete de Shimura associee a une donnee de Shimura (G, X) pour un groupe algebrique adjoint sur Q et une G(R)-classe de conjugaison X de morphismes:
Zeev Rudnick - One of the best experts on this subject based on the ideXlab platform.
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small scale Equidistribution of eigenfunctions on the torus
Communications in Mathematical Physics, 2017Co-Authors: Stephen Lester, Zeev RudnickAbstract:We study the small scale distribution of the L2 mass of eigenfunctions of the Laplacian on the flat torus \({\mathbb{T}^{d}}\). Given an orthonormal basis of eigenfunctions, we show the existence of a density one subsequence whose L2 mass equidistributes at small scales. In dimension two our result holds all the way down to the Planck scale. For dimensions d = 3, 4 we can restrict to individual eigenspaces and show small scale Equidistribution in that context. We also study irregularities of quantum Equidistribution: We construct eigenfunctions whose L2 mass does not equidistribute at all scales above the Planck scale. Additionally, in dimension d = 4 we show the existence of eigenfunctions for which the proportion of L2 mass in small balls blows up at certain scales.
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the variance of the number of prime polynomials in short intervals and in residue classes
arXiv: Number Theory, 2012Co-Authors: Jonathan P Keating, Zeev RudnickAbstract:We resolve a function field version of two conjectures concerning the variance of the number of primes in short intervals (Goldston and Montgomery) and in arithmetic progressions (Hooley). A crucial ingredient in our work are recent Equidistribution results of N. Katz.
Juan Riveraletelier - One of the best experts on this subject based on the ideXlab platform.
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Equidistribution quantitative des points de petite hauteur sur la droite projective
Mathematische Annalen, 2006Co-Authors: Charles Favre, Juan RiveraletelierAbstract:We introduce a new class of adelic heights on the projective line. We estimate their essential minimum and prove a result of Equidistribution (at every place) for points of small height with estimates on the speed of convergence. To each rational function R in one variable and defined over a number field K, is associated a normalized height on the algebraic closure of K. We show that these dynamically defined heights are adelic in our sense, and deduce from this Equidistribution results for preimages of points under R at every place of K. Our approach follows that of Bilu, and relies on potential theory in the complex plane, as well as in the Berkovich space associated to the projective line over Open image in new window, for each prime p.
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Equidistribution quantitative des points de petite hauteur sur la droite projective
arXiv: Number Theory, 2004Co-Authors: Charles Favre, Juan RiveraletelierAbstract:We introduce a new class of adelic heights on the projective line. We estimate their essential minimum and prove a result of Equidistribution (at every place) for points of small height with estimates on the speed of convergence. To each rational function R in one variable and defined over a number field K, is associated a normalized height on the algebraic closure of K. We show that these dynamically defined heights are adelic in our sense, and deduce from this Equidistribution results for preimages of points under R at every place of K. Our approach follows that of Bilu, and relies on potential theory in the complex plane, as well as in the Berkovich space associated to the projective line over C_p, for each prime p.
Laurent Clozel - One of the best experts on this subject based on the ideXlab platform.
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Equidistribution de sous varietes speciales
Annals of Mathematics, 2005Co-Authors: Laurent Clozel, Emmanuel UllmoAbstract:de points speciaux (les points a multiplication complexe) et un ensemble de sous-varietes speciales que l'on appelle sous-varietes de type de Hodge. Les definitions qui seront donnees plus tard dans le texte sont presentees de maniere tres agreable dans le papier de Moonen [8]. Dans ce cadre Andre et Oort font la conjecture suivante. Soit Y une sousvariete de S, il existe un ensemble fini {S1,..., Sr} de sous-varietes speciales avec Si C Y pour tout i tel que toute variete speciale Z de S contenue dans Y est en fait contenue dans un des Si. Le resultat le plus profond dans la direction de cette conjecture a ete obtenu par Edixhoven et Yafaev [5]. On definit dans ce texte une classe assez large de sous-varietes speciales que nous appellerons fortement speciales par manque d'une terminologie plus adequate. Decrivons les sous-varietes fortement speciales: Soit S une variete de Shimura associee a une donnee de Shimura (G, X) pour un groupe algebrique adjoint sur Q et une G(R)-classe de conjugaison X de morphismes:
