منابع مشابه
8 Mass Equidistribution for Hecke Eigenforms
X |φ(z)|2 dx dy y = 1. Zelditch [19] has shown that as λ → ∞, for a typical Maass form φ the measure μφ := |φ(z)|2 dx dy y approaches the uniform distribution measure 3 π dx dy y . This statement is referred to as “Quantum Ergodicity.” Rudnick and Sarnak [13] have conjectured that an even stronger result holds. Namely, that as λ → ∞, for every Maass form φ the measure μφ approaches the uniform ...
متن کاملMass Equidistribution for Automorphic Forms of Cohomological Type on Gl2
One of the central problems in the subject of quantum chaos is to understand the behaviour of high energy Laplace eigenfunctions on a Riemannian manifold M . There is an important conjecture of Rudnick and Sarnak [32] which predicts one aspect of this behaviour in the case when M is compact and negatively curved, namely that the microlocal lifts of eigenfunctions tend weakly to Liouville measur...
متن کاملBlock Sieving Algorithms Block Sieving Algorithms
Quite similiar to the Sieve of Erastosthenes, the best-known general algorithms for fac-toring large numbers today are memory-bounded processes. We develop three variations of the sieving phase and discuss them in detail. The fastest modiication is tailored to RISC processors and therefore especially suited for modern workstations and massively parallel supercomputers. For a 116 decimal digit c...
متن کاملEquidistribution Questions for Universal Extensions
Let k be a field, C/k a proper, smooth, geometrically connected curve of genus g ≥ 1 given with a marked rational point 0 ∈ C(k), JC/k := Pic 0 C/k its Jacobian. Concretely, the group JC(k) is the group (under tensor product) of isomorphism classes of invertible sheaves L on C of degree zero. Given a point P ∈ C(k), we denote by I(P ) ⊂ OC the ideal sheaf of functions vanishing at P . Given P1,...
متن کاملLocalized quantitative criteria for equidistribution
Let (xn)n=1 be a sequence on the torus T (normalized to length 1). We show that if there exists a sequence of positive real numbers (tn)n=1 converging to 0 such that lim N→∞ 1 N2 N ∑ m,n=1 1 √ tN exp ( − 1 tN (xm − xn) ) = √ π, then (xn)n=1 is uniformly distributed. This is especially interesting when tN ∼ N−2 since the size of the sum is then essentially determined exclusively by local gaps at...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2010
ISSN: 0003-486X
DOI: 10.4007/annals.2010.172.1499