On the equidistribution of hecke points
WebThen we have equidistribution of Hecke points over the modular surface: lim n → ∞ [ T n f] ( z) = ∫ X ( 1) f ( z) d z Both of these results have Hecke's name attached. The first deals with Hecke characters and L-functions the second deals with …
On the equidistribution of hecke points
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Webbe the orthonormal basis of Hecke eigenforms in S 2k((1)), the space of holomorphic cusp forms of weight 2kwith respect to the modular group (1). Thus J k=dim C S 2k((1)) = ˆ [k=6] 1; if k 1(mod6); [k=6]; if k6 1(mod6): One expects that the following equidistribution law holds for f j;k as the weight k!1: for any measurable subset Aon the ... WebThe crux is a geometric expansion of the crosscorrelation between the periodic measure on a torus orbit and a Hecke correspondence, expressing it as a short shifted convolution sum. The latter is bounded from above generalizing the method of Shiu and Nair to polynomials in two variables on smooth domains. Original language.
Web13 de jan. de 2003 · On the equidistribution of Hecke points A semicontinuity result for … Web1 de nov. de 2007 · Given the orthonormal basis of Hecke eigenforms in S 2k (Γ ), one …
Web8 de fev. de 2024 · In this paper we characterize all the sequences of discriminants for … Web13 de jan. de 2003 · TLDR. This article tries to model the average case of lattice reduction algorithms, starting with the celebrated Lenstra-Lenstra-Lovasz algorithm (L3), and discusses what is meant by lattice Reduction on the average, and presents extensive …
Web28 de mar. de 2024 · Joint equidistribution of CM points. Event details. Date: 28.03.2024 – 16:15 › 17:15 : Speaker: Ilya Khayutin (Princeton) Location: ... As a result the obstacle to proving equidistribution is the potential concentration of mass on graphs of Hecke correspondences and translates thereof.
Web17 de nov. de 2006 · As a corollary, we generalize the equidistribution result of Hecke points ( [COU], [EO1]) to homogeneous spaces G / H. As a concrete application, we describe the equidistribution result in the rational matrices with a given characteristic polynomial. Download to read the full article text Author information Hee Oh bj\\u0027s brewhouse bethel parkWeb12 de out. de 2024 · Joint Equidistribution of CM Points. We prove the mixing … bj\u0027s brewhouse blondeWebequidistribution of mass of the respective eigenfunction since they estimate the ex tent to which the eigenfunctions may localize in small sets. The problem of bound ing sup-norms is also closely related to the multiplicity problem: if V\ denotes the eigenspace of the eigenvalue A, then we have the inequality [Sar] dim Va < vol(X) sup \\F\\i ... bj\u0027s brewhouse birthdayWeb12 de jan. de 2024 · Eskin, A. and Oh, H., Ergodic theoretic proof of equidistribution of Hecke points, Ergodic Theory Dynam. Systems 26 ( 2006 ), 163 – 167 . CrossRef Google Scholar bj\\u0027s brewhouse beltline addisonWebBy a CM-suborbit O(x) of a CM-point we mean an orbit O(x) ⊂ O cm(x) under an open subgroup of T(Q)\T(Q ).Itsconductor c(O(x)) is defined to be the largest ideal cso that (1+ cO K)× stabilizes O(x). The equidistribution conjecture implies the equidistribution of O cm(x). Theorem 3.1. Let x i be a sequence of CM-points on M U. Then the CM ... dating my friends crushWebThe main tool in the proof of Theorem 1.4 is the use of Hecke operators. The relation of Hecke operators to Linnik’s problem was first observed by Sarnak in [Sa]. Our starting point is then an equidistribution result for Hecke points in ZΓ\Gwhere Zis the connected center of Gand Γ is a congruence subgroup of G. This result was dating my daughter version 33Web3. Equidistribution of intersection points 15 4. The pull-push form 19 5. Inarianvt forms on period domains 24 6. Applications 35 References 48 1. Introduction Let Gbe a semi-simple Lie group and let Γ ⊂Gbe a lattice. Homogeneous dynamics is traditionally interested in the equidistribution properties of the orbits of a Lie subgroup bj\\u0027s brewhouse blonde