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.

Voir la notice de l'article provenant de la source EMS Press

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
Mots-clés : Zeros of modular forms, mass equidistribution, automorphic forms 
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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. https://geodesic-test.mathdoc.fr/articles/10.4171/jems/794/

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