Geodesic
Weyl-type hybrid subconvexity bounds for twisted $L$-functions and Heegner points on shrinking sets
Journal of the European Mathematical Society, Tome 19 (2017) no. 5, pp. 1545-1576 Cet article a éte moissonné depuis la source EMS Press

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Let q be odd and squarefree, and let χq​ be the quadratic Dirichlet character of conductor q. Let uj​ be a Hecke–Maass cusp form on Γ0​(q) with spectral parameter tj​. By an extension of work of Conrey and Iwaniec, we show L(uj​×χq​,1/2)≪ε​(q(1+∣tj​∣))1/3+ε, uniformly in both q and tj​. A similar bound holds for twists of a holomorphic Hecke cusp form of large weight k. Furthermore, we show that ∣L(1/2+it,χq​)∣≪ε​((1+∣t∣)q)1/6+ε, improving on a result of Heath–Brown.
DOI : 10.4171/jems/699
Classification : 11-XX
Keywords: Subconvexity, L-functions, equidistribution, Heegner points 
@article{JEMS_2017_19_5_a6,
     author = {Matthew P. Young},
     title = {Weyl-type hybrid subconvexity bounds for twisted $L$-functions and {Heegner} points on shrinking sets},
     journal = {Journal of the European Mathematical Society},
     pages = {1545--1576},
     year = {2017},
     volume = {19},
     number = {5},
     doi = {10.4171/jems/699},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/699/}
}
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Matthew P. Young. Weyl-type hybrid subconvexity bounds for twisted $L$-functions and Heegner points on shrinking sets. Journal of the European Mathematical Society, Tome 19 (2017) no. 5, pp. 1545-1576. doi: 10.4171/jems/699

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