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Bounds for Average toward the Resonance Barrier for GL(3) × GL(2) Automorphic Forms.
- Source :
-
Acta Mathematica Sinica . Sep2023, Vol. 39 Issue 9, p1667-1683. 17p. - Publication Year :
- 2023
-
Abstract
- Let f be a fixed Maass form for SL3 (ℤ) with Fourier coefficients Af(m, n). Let g be a Maass cusp form for SL2 (ℤ) with Laplace eigenvalue 1 4 + k 2 and Fourier coefficient λg(n), or a holomorphic cusp form of even weight k. Denote by SX(f × g, α, β) a smoothly weighted sum of Af(1, n)λg(n)e(αnβ) for X < n < 2X, where α ≠ 0 and β > 0 are fixed real numbers. The subject matter of the present paper is to prove non-trivial bounds for a sum of SX(f × g, α, β) over g as k tends to ∞ with X. These bounds for average provide insight for the corresponding resonance barriers toward the Hypothesis S as proposed by Iwaniec, Luo, and Sarnak. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 39
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 172284544
- Full Text :
- https://doi.org/10.1007/s10114-023-1022-4