Weyl-type hybrid subconvexity bounds for twisted L-functions and Heegner points on shrinking sets Academic Article uri icon


  • European Mathematical Society 2017. Let q be odd and squarefree, and let Xq be the quadratic Dirichlet character of conductor q. Let uj be a Hecke-Maass cusp form on 0(q) with spectral parameter tj . By an extension of work of Conrey and Iwaniec, we show L(uj q ; 1/2) (q(1 + |tj|))1/3+, 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; Xq)| ((1 + |t|/q)1/6+, 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.

published proceedings


altmetric score

  • 0.25

author list (cited authors)

  • Young, M. P.

citation count

  • 39

complete list of authors

  • Young, Matthew P

publication date

  • January 2017