Geodesic
On the Distribution of Satake Parameters for Siegel Modular Forms
Documenta mathematica, Tome 24 (2019), pp. 677-747.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We prove a harmonically weighted equidistribution result for the $p$-th Satake parameters of the family of automorphic cuspidal representations of $\operatorname{PGSp}(2n)$ of fixed weight $\mathtt{k}$ and prime-to-$p$ level $N\to \infty$. The main tool is a new asymptotic Petersson formula for $\operatorname{PGSp}(2n)$ in the level aspect.
Classification : 11F46, 11F25, 11F30, 11F70, 11F72
Keywords: Siegel modular forms, Petersson formula, Satake parameters 
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     author = {Knightly, Andrew and Li, Charles},
     title = {On the {Distribution} of {Satake} {Parameters} for {Siegel} {Modular} {Forms}},
     journal = {Documenta mathematica},
     pages = {677--747},
     publisher = {mathdoc},
     volume = {24},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a43/}
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Knightly, Andrew; Li, Charles. On the Distribution of Satake Parameters for Siegel Modular Forms. Documenta mathematica, Tome 24 (2019), pp. 677-747. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a43/