Geodesic
PERIODIC TWISTS OF $\operatorname{GL}_{3}$-AUTOMORPHIC FORMS
Forum of Mathematics, Sigma, Tome 8 (2020)

Voir la notice de l'article provenant de la source Cambridge University Press

We prove that sums of length about $q^{3/2}$ of Hecke eigenvalues of automorphic forms on $\operatorname{SL}_{3}(\mathbf{Z})$ do not correlate with $q$-periodic functions with bounded Fourier transform. This generalizes the earlier results of Munshi and Holowinsky–Nelson, corresponding to multiplicative Dirichlet characters, and applies, in particular, to trace functions of small conductor modulo primes. 
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     author = {EMMANUEL KOWALSKI and YONGXIAO LIN and PHILIPPE MICHEL and WILL SAWIN},
     title = {PERIODIC {TWISTS} {OF} $\operatorname{GL}_{3}${-AUTOMORPHIC} {FORMS}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {8},
     year = {2020},
     doi = {10.1017/fms.2020.7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2020.7/}
}
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EMMANUEL KOWALSKI; YONGXIAO LIN; PHILIPPE MICHEL; WILL SAWIN. PERIODIC TWISTS OF $\operatorname{GL}_{3}$-AUTOMORPHIC FORMS. Forum of Mathematics, Sigma, Tome 8 (2020). doi: 10.1017/fms.2020.7

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