Restrictions of Eisenstein series and Rankin-Selberg convolution

2017/06/28 by Rodney Keaton, Keaton, Rodney, Ameya Pitale +1 · 1 citation
Mathematics · #11F41 #11F70 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1706.09342

openalex publication_date 2017/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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