The spectral decomposition of shifted convolution sums

Abstract

We obtain a spectral decomposition of shifted convolution sums in Hecke eigenvalues of holomorphic or Maass cusp forms.

15 pages, LaTeX2e; v2: corrected and slightly expanded version

References in corpus (2)

• An additive problem in the Fourier coefficients of cusp forms
• New bounds for automorphic L-functions

Cited by in corpus (23)

• The subconvexity problem for $\GL_{2}$
• The second moment of twisted modular L-functions
• Twisted L-functions over number fields and Hilbert's eleventh problem
• Shifted convolution sums for $GL(3)\times GL(2)$
• Linnik's ergodic method and the distribution of integer points on spheres
• Level Aspect Subconvexity For Rankin-Selberg $L$-functions
• Burgess-like subconvexity for ${\mathrm{GL}}_1$
• The horocycle flow at prime times
• Triple Correlation Sums of Coefficients of Cusp Forms
• Shifted convolution sums and Burgess type subconvexity over number fields
• The Laplace Transform of the Second Moment in the Gauss Circle Problem
• Zeros of ${\mathrm{GL}}_2$ $L$-functions on the critical line
• Transition Mean Values of Shifted Convolution Sums
• Local integral transforms and global spectral decomposition
• Twisted Hilbert modular L-functions and spectral theory
• Some analytic aspects of automorphic forms on GL(2) of minimal type
• On the binary additive divisor problem in mean
• A shifted convolution sum for $GL(3)\times GL(2)$
• Nonvanishing of self-dual $L$-values via spectral decomposition of shifted convolution sums
• Shifted convolution sums and Eisenstein series formed with modular symbols
• On the shifted convolution problem in mean
• Asymptotic bounds for special values of shifted convolution Dirichlet series
• Quadratic Hecke sums and mass equidistribution