Restrictions of Eisenstein Series and Rankin-Selberg Convolution
Copyright policy )Restrictions of Eisenstein Series and Rankin-Selberg Convolution
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.
- University of Oklahoma United States
- East Tennessee State University United States
Mathematics and Statistics, Mathematics - Number Theory, FOS: Mathematics, 11F70, 11F41, Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Number Theory (math.NT), Waldspurger model, 510, Hilbert modular forms
Mathematics and Statistics, Mathematics - Number Theory, FOS: Mathematics, 11F70, 11F41, Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Number Theory (math.NT), Waldspurger model, 510, Hilbert modular forms
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