Twisted L-functions over number fields and Hilbert's eleventh problem

Abstract

We prove a Burgess-like subconvex bound for twisted L-functions of a fixed irreducible cuspidal automorphic representation of GL(2) over a totally real number field. The proof is based on a spectral decomposition of shifted convolution sums and a generalized Kuznetsov formula.

44 pages, LaTeX2e, submitted; v2: Introduction revised, minor changes elsewhere; v3: Small corrections and additions

References in corpus (1)

• The subconvexity problem for $\GL_{2}$

Cited by in corpus (28)

• Burgess-like subconvex bounds for $G{L}_2\times G{L}_1$
• Twisted moments of L-functions and spectral reciprocity
• Bounds for eigenforms on arithmetic hyperbolic 3-manifolds
• Torsion homology growth and cycle complexity of arithmetic manifolds
• Subconvex equidistribution of cusp forms: reduction to Eisenstein observables
• Mass equidistribution of Hilbert modular eigenforms
• Eisenstein series and the cubic moment for PGL(2)
• On basic and Bass quaternion orders
• Subconvexity for sup-norms of automorphic forms on PGL(n)
• Burgess-like subconvexity for ${\mathrm{GL}}_1$
• A Note on Riemann Surfaces of Large Systole
• A semi-adelic Kuznetsov formula over number fields
• Rankin-Selberg L-functions in cyclotomic towers, III
• Zeros of ${\mathrm{GL}}_2$ $L$-functions on the critical line
• Explicit subconvexity for ${\mathrm{GL}}_2$
• Explicit Burgess-like subconvex bounds for ${\mathrm{GL}}_2\times {\mathrm{GL}}_1$
• Twisted Hilbert modular L-functions and spectral theory
• Mordell-Weil growth for GL2-type abelian varieties over Hilbert class fields of CM fields
• Subconvexity for $L$-Functions on ${\mathrm{GL}}_3$ over Number Fields
• On Weyl's Subconvex Bound for Cube-Free Hecke characters: Totally Real Case
• Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables
• On the Waldspurger Formula and the Metaplectic Ramanujan Conjecture over Number Fields
• Joint distribution of eigenvalues of Hecke and Casimir operators for Hilbert Maass forms
• Kuznetsov's trace formula and the Hecke eigenvalues of Maass forms
• Integral presentations of the shifted convolution problem and subconvexity estimates for ${\mathrm{GL}}_n$-automorphic $L$-functions
• The Sup-norm of Holomorphic Cusp Forms
• Class group twists and Galois averages of ${\mathrm{GL}}_n$-automorphic $L$-functions
• Nonvanishing of self-dual $L$-values via spectral decomposition of shifted convolution sums