Webequidistribution of Hecke points may follow from Ratner’s measure classi cation the-orem [Ra] provided ai’s converge to an element not belonging to Comm(). However Burger and Sarnak did not give a detailed proof of this claim: this was done by Dani and Margulis [DM, Corollary 6.2] in 1993, where they deduced the assertion from their 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 ...
Equidistribution of Hecke points on the supersingular module
WebHecke equidistribution. For a prime p ≡ 1 ( mod 4), we can write p = a 2 + b 2 = N ( a + b i). Therefore. where φ ∈ [ 0, 2 π]. I know that Hecke proved that φ is equidistributed. I am looking for a reference for this nice result. I would be thankful if one can give me a reference. Web8 de fev. de 2024 · In this paper we characterize all the sequences of discriminants for … solway driver training
Ergodic theoretic proof of equidistribution of Hecke points
Webintersection of any finite-rank subgroup of A with the set of points on A corresponding to an isogeny class on S is finite. The question was proposed by A. Buium and B. Poonen in 2009. We follow the strategy proposed by the authors, using a result about the equidistribution of Hecke points on Shimura varieties and Serre’s open image theorem. WebThis set of lectures provides a structured introduction to the concept of equidistribution in number theory. This concept is of growing importance in many areas, including cryptography, zeros of L-functions, Heegner points, prime number theory, the theory of quadratic forms, and the arithmetic aspects of quantum chaos. Web18 de nov. de 2000 · Hecke Operators and Equidistribution of Hecke Points Authors: Laurent Clozel Hee Oh Emmanuel Ullmo Université Paris-Sud 11 Abstract a are commensurable with each other and j n a j = [ : a 1 a],... small business bank account uk