Weyl-type hybrid subconvexity bounds for twisted -functions and Heegner points on shrinking sets
Matthew P. Young
Texas A&M University, College Station, USA
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Abstract
Let be odd and squarefree, and let be the quadratic Dirichlet character of conductor . Let be a Hecke–Maass cusp form on with spectral parameter . By an extension of work of Conrey and Iwaniec, we show , uniformly in both and . A similar bound holds for twists of a holomorphic Hecke cusp form of large weight . Furthermore, we show that , improving on a result of Heath–Brown.
As a consequence of these new bounds, we obtain explicit estimates for the number of Heegner points of large odd discriminant in shrinking sets.
Cite this article
Matthew P. Young, Weyl-type hybrid subconvexity bounds for twisted -functions and Heegner points on shrinking sets. J. Eur. Math. Soc. 19 (2017), no. 5, pp. 1545–1576
DOI 10.4171/JEMS/699