Double weighted sum involving GL(2) Fourier coefficients

Key Points

• This research aims to establish estimates for bilinear sums involving Fourier coefficients of cusp forms.
• Analyzes Fourier coefficients of Hecke-holomorphic and Hecke-Maass cusp forms for SL(2).
• Proves non-trivial estimates for bilinear sums.
• Explores shifted convolution sums and summatory functions as corollaries.
• Demonstrated new estimates for bilinear sums involving these Fourier coefficients.
• Established interesting bounds for shifted convolution sums.
• Provided new insights into summatory functions related to these forms.