Geodesic
Small scale distribution of zeros and mass of modular forms
Journal of the European Mathematical Society, Tome 20 (2018) no. 7, pp. 1595-1627 Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

We study the behavior of zeros and mass of holomorphic Hecke cusp forms on SL2​(Z)\H at small scales. In particular, we examine the distribution of the zeros within hyperbolic balls whose radii shrink sufficiently slowly as k→∞. We show that the zeros equidistribute within such balls as k→∞ as long as the radii shrink at a rate at most a small power of 1/logk. This relies on a new, effective, proof of Rudnick's theorem on equidistribution of the zeros and on an effective version of Quantum Unique Ergodicity for holomorphic forms, which we obtain in this paper.
DOI : 10.4171/jems/794
Classification : 11-XX, 58-XX
Keywords: Zeros of modular forms, mass equidistribution, automorphic forms 
@article{JEMS_2018_20_7_a1,
     author = {Stephen Lester and Kaisa Matom\"aki and Maksym Radziwi{\l}{\l}},
     title = {Small scale distribution of zeros and mass of modular forms},
     journal = {Journal of the European Mathematical Society},
     pages = {1595--1627},
     year = {2018},
     volume = {20},
     number = {7},
     doi = {10.4171/jems/794},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/794/}
}
TY  - JOUR
AU  - Stephen Lester
AU  - Kaisa Matomäki
AU  - Maksym Radziwiłł
TI  - Small scale distribution of zeros and mass of modular forms
JO  - Journal of the European Mathematical Society
PY  - 2018
SP  - 1595
EP  - 1627
VL  - 20
IS  - 7
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/794/
DO  - 10.4171/jems/794
ID  - JEMS_2018_20_7_a1
ER  - 
%0 Journal Article
%A Stephen Lester
%A Kaisa Matomäki
%A Maksym Radziwiłł
%T Small scale distribution of zeros and mass of modular forms
%J Journal of the European Mathematical Society
%D 2018
%P 1595-1627
%V 20
%N 7
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/794/
%R 10.4171/jems/794
%F JEMS_2018_20_7_a1
Stephen Lester; Kaisa Matomäki; Maksym Radziwiłł. Small scale distribution of zeros and mass of modular forms. Journal of the European Mathematical Society, Tome 20 (2018) no. 7, pp. 1595-1627. doi: 10.4171/jems/794

Cité par Sources :