Geodesic
Restrictions of Eisenstein Series and Rankin-Selberg Convolution
Documenta mathematica, Tome 24 (2019), pp. 1-45
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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.
DOI : 10.4171/dm/673
Classification : 11F41, 11F67
Mots-clés : Hilbert modular forms, Waldspurger model 
@article{10_4171_dm_673,
     author = {Rodney Keaton and Ameya Pitale},
     title = {Restrictions of {Eisenstein} {Series} and {Rankin-Selberg} {Convolution}},
     journal = {Documenta mathematica},
     pages = {1--45},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/673},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/673/}
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Rodney Keaton; Ameya Pitale. Restrictions of Eisenstein Series and Rankin-Selberg Convolution. Documenta mathematica, Tome 24 (2019), pp. 1-45. doi: 10.4171/dm/673

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