Keaton, Rodney; Pitale, Ameya

Restrictions of Eisenstein Series and Rankin-Selberg Convolution

Doc. Math. 24, 1-45 (2019)
DOI: 10.25537/dm.2019v24.1-45

Summary

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.

Mathematics Subject Classification

11F41, 11F67

Keywords/Phrases

Hilbert modular forms, Waldspurger model

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Affiliation

Keaton, Rodney
Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN 37614, USA
Pitale, Ameya
Department of Mathematics, University of Oklahoma, Norman, OK 73019 USA

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