A generalized cubic moment and the Petersson formula for newforms

Abstract

Using a cubic moment, we prove a Weyl-type subconvexity bound for the quadratic twists of a holomorphic newform of square-free level, trivial nebentypus, and arbitrary even weight. This generalizes work of Conrey and Iwaniec in that the newform that is being twisted may have arbitrary square-free level, and also that the quadratic character may have even conductor. One of the new tools developed in this paper is a more general Petersson formula for newforms of square-free level.

Final version; to appear in Math. Annalen

References in corpus (3)

• Explicit calculations with Eisenstein series
• Oscillatory integrals with uniformity in parameters
• The first non-vanishing quadratic twist of an automorphic L-series

Cited by in corpus (20)

• The fourth moment of Dirichlet $L$-functions along a coset and the Weyl bound
• Oscillatory integrals with uniformity in parameters
• Explicit calculations with Eisenstein series
• Modular invariants for real quadratic fields and Kloosterman sums
• Eisenstein series and the cubic moment for PGL(2)
• Optimal Small Scale Equidistribution of Lattice Points on the Sphere, Heegner Points, and Closed Geodesics
• Burgess-like subconvexity for ${\mathrm{GL}}_1$
• The Fifth Moment of modular L-functions
• Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite field
• Mixed moment of $GL(2)$ and $GL(3)$ $L$-functions
• Jacobi forms, Saito-Kurokawa lifts, their Pullbacks and sup-norms on average
• Weyl-type bounds for twisted $GL(2)$ short character sums
• Mass equidistribution for Saito-Kurokawa lifts
• On the Waldspurger Formula and the Metaplectic Ramanujan Conjecture over Number Fields
• Subconvexity bounds for twisted L-functions, II
• On subconvexity bounds for twisted L-functions
• Strong Hybrid Subconvexity for Twisted Selfdual ${\mathrm{GL}}_3$ $L$-Functions
• Intersecting geodesics on the modular surface
• A Note on Holomorphic Quantum Unique Ergodicity
• Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions II: The Eisenstein Case