Subconvexity and equidistribution of Heegner points in the level aspect Academic Article uri icon

abstract

  • AbstractLet $q$ be a prime and $- Dlt - 4$ be an odd fundamental discriminant such that $q$ splits in $ mathbb{Q} ( sqrt{- D} )$. For $f$ a weight-zero HeckeMaass newform of level $q$ and ${Theta }_{chi } $ the weight-one theta series of level $D$ corresponding to an ideal class group character $chi $ of $ mathbb{Q} ( sqrt{- D} )$, we establish a hybrid subconvexity bound for $L(f imes {Theta }_{chi } , s)$ at $s= 1/ 2$ when $qasymp {D}^{eta } $ for $0lt eta lt 1$. With this circle of ideas, we show that the Heegner points of level $q$ and discriminant $D$ become equidistributed, in a natural sense, as $q, D
    ightarrow infty $
    for $qleq {D}^{1/ 20- varepsilon } $. Our approach to these problems is connected to estimating the ${L}^{2} $-restriction norm of a Maass form of large level $q$

published proceedings

  • COMPOSITIO MATHEMATICA

altmetric score

  • 0.25

author list (cited authors)

  • Liu, S., Masri, R., & Young, M. P.

citation count

  • 14

complete list of authors

  • Liu, Sheng-Chi||Masri, Riad||Young, Matthew P

publication date

  • January 1, 2013 11:11 AM

publisher