In a 2005 paper, Yang constructed families of Hilbert Eisenstein series, which when restricted to the diagonal are conjectured to span the underlying space of elliptic modular forms. One approach to these conjectures is to show the non-vanishing of an inner product of elliptic eigenforms with the restrictions of Eisenstein series. In this paper, we compute this inner product locally by using explicit values of new vectors in the Waldspurger model.
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Rodney Keaton, Ameya Pitale, Restrictions of Eisenstein Series and Rankin-Selberg Convolution. Doc. Math. 24 (2019), pp. 1–45DOI 10.4171/DM/673