Base change lift type spinor L-feeetion of GSp_2(Q)

摘要

In [4], we happened to consturct Siegel modular cuspform F and non-cuspform E of degree 2 having the same spinor L-function: Lspin(s, E) = Lspin(s, F), which is equal to the Hasse-Weil zeta function of hyper-elliptic curve y2 - x5 - x. The CAP representation has a L-function of a non-cuspidal one, but, our phenomenon is not the case. In this article, we consider the problem 'What type of spinor L-iunction is related to cuspform and non-cuspform, simultaneously?'. To do it, we will classify the spinor L-iunctions of non-cuspforms. The classical 'Zharkovskaya relation' describes L-function of Siegel non-cuspform by that of the elliptic modular form obtained by the Siegel operator, as follows.