Non-linear Additive Twists of GL(3) × GL(2) and GL(3) Maass Forms
Article Type
Research Article
Publication Title
Monatshefte fur Mathematik
Abstract
Let λπ(r, n) be the Fourier coefficients of a Hecke-Maass cusp form π for SL(3 , Z) and λf(n) be the Fourier coefficients of a Hecke-eigen form f for SL(2 , Z). The aim of this article is to get a non-trivial bound on the sum which is non-linear additive twist of the coefficients λπ(m, n) and λf(n). More precisely, we have ∑n=1∞λπ(r,n)e(αnβ)V(nX)≪π,ϵαβr76X34+9β28+ϵ.and ∑n=1∞λπ(r,n)λf(n)e(αnβ)V(nX)≪π,f,ϵ(αβ)32rX34+29β44+ϵ,where V(x) is a smooth function supported in [1, 2] and satisfying V(j)(x) ≪ j1.
First Page
315
Last Page
361
DOI
10.1007/s00605-022-01725-x
Publication Date
10-1-2022
Recommended Citation
Kumar, Sumit; Mallesham, Kummari; and Singh, Saurabh Kumar, "Non-linear Additive Twists of GL(3) × GL(2) and GL(3) Maass Forms" (2022). Journal Articles. 2950.
https://digitalcommons.isical.ac.in/journal-articles/2950