On the symmetric fourth power \(L\)-function of \(GL_ 2\)
Let \(G= \text{GL}(2)\) and let \(r\) be the symmetric fourth power representation of the \(L\)-group \(\text{GL}(2, \mathbb{C})\) of \(G\). The author intends to prove that, given a cuspidal representation \(\pi\) of \(\text{GL}(2, \mathbb{A})\), the partial \(L\)-function \(L_S(\pi\otimes \chi, r)\) is holomorphic for generic \(\chi\). In this paper, he introduces a Rankin-Selberg type integral for this \(L\)-function, which involves an Eisenstein series on the double cover of a group of type \(G_2\) and a theta function. This integral is a product of local factors, which are computed at almost all places, and a non-vanishing result is proved. The rest will follow in another article (or articles).
scientific article; zbMATH DE number 836160