Back to Search
Start Over
A shifted convolution sum for GL(3)×GL(2) with weighted average.
- Source :
- Ramanujan Journal; May2024, Vol. 64 Issue 1, p93-122, 30p
- Publication Year :
- 2024
-
Abstract
- In this paper, we will prove a non-trivial bound for the weighted average version of a shifted convolution sum for G L (3) × G L (2) , i.e. for arbitrary small ϵ > 0 and X 1 / 4 + δ ≤ H ≤ X with δ > 0 , we prove 1 H ∑ h = 1 ∞ λ f (h) V h H ∑ n = 1 ∞ λ π (1 , n) λ g (n + h) W n X ≪ X 1 - δ + ϵ , where V, W are smooth and compactly supported functions, λ f (n) , λ g (n) and λ π (1 , n) are the normalized n-th Fourier coefficients of holomorphic or Hecke–Maass cusp forms f, g for S L (2 , Z) , and Hecke–Maass cusp form π for S L (3 , Z) . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 13824090
- Volume :
- 64
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Ramanujan Journal
- Publication Type :
- Academic Journal
- Accession number :
- 176999620
- Full Text :
- https://doi.org/10.1007/s11139-023-00815-0