منابع مشابه
Fourier Coefficients of Hecke Eigenforms
We provide systematic evaluations, in terms of binary quadratic representations of 4p, for the p-th Fourier coefficients of each member f of an infinite class C of CM eigenforms. As an application, previously conjectured evaluations of three algebro-geometric character sums can now be formulated explicitly without reference to eigenforms. There are several non-CM newforms that appear to share s...
متن کاملHecke eigenforms with rational coefficients and complex multiplication
We prove that, assuming GRH, there are only finitely many newforms with rational Fourier coefficients and complex multiplication for fixed weight up to twisting. We produce tables of such forms for weights 3 and 4, where this finiteness holds unconditionally. We also comment on geometric realizations.
متن کاملQuantum Variance for Hecke Eigenforms ✩
– We calculate the quantum variance for the modular surface. This variance, introduced by S. Zelditch, describes the fluctuations of a quantum observable. The resulting quadratic form is then compared with the classical variance. The expectation that these two coincide only becomes true after inserting certain subtle arithmetic factors, specifically the central values of corresponding L-functio...
متن کامل8 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 کاملHecke eigenforms and the arithmetic of singular K 3 surfaces ”
for the dissertation ”Hecke eigenforms and the arithmetic of singular K3 surfaces”
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ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2012
ISSN: 0208-6573
DOI: 10.7169/facm/2012.46.2.1