On the modularity of the \(\text{GL}_2\)-twisted spinor \(L\)-function
In this paper, the author studies the twisted spinor \(L\)-function \(Z_{G\otimes h}(s)\) attached to Hecke eigenforms \(G\in M_{k_1}^2\) (degree 2, weight \(k_1\)) and \(h\in M_{k_2}^1\) (degree 1, weight \(k_2\)). He proves the followings: 1) The \(L\)-function \(Z_{G\otimes h}(s)\) has a meromorphic continuation to the whole complex plane and possesses a functional equation. 2) Let \(E_k^n\) be the Siegel-Eisenstein series of degree \(n\) and weight \(k\). Then \(Z_{E_k^2\otimes E_{2k-2}^1}(s)\) is modular. Here the modularity of \(Z_{G\otimes h}(s)\) means that there exists a Siegel modular form \(F:=G\boxtimes h\) of degree 3 such that \(L(s,G\boxtimes h)=Z_{G\otimes h}(s)\). Moreover, he refers to the Miyawaki conjecture concerning with Siegel modular forms of degree 3.
scientific article; zbMATH DE number 5723791
scientific article