Cuspidal part of an Eisenstein series restricted to an index 2 subfield

Yueke Hu ETH Zürich, HG GO 68.2, Rämistrasse 101, 8092 Zurich, Switzerland

Number Theory mathscidoc:2206.24006

Research in Number Theory, 2, (33), 2016.11
Let E be a quadratic algebra over a number field F. Let E(g, s) be an Eisenstein series on GL2(E), and let F be a cuspidal automorphic form on GL2(F). We will consider in this paper the following automorphic integral: ∫ZAGL2(F)∖GL2(AF)F(g)E(g,s)dg. This is in some sense the complementary case to the well-known Rankin–Selberg integral and the triple product formula. We will approach this integral by Waldspurger’s formula, giving a criterion about when the integral is automatically zero, and otherwise the L-functions it represents. We will also calculate the local integrals at some ramified places, where the level of the ramification can be arbitrarily large.
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@inproceedings{yueke2016cuspidal,
  title={Cuspidal part of an Eisenstein series restricted to an index 2 subfield},
  author={Yueke Hu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626173409300224480},
  booktitle={Research in Number Theory},
  volume={2},
  number={33},
  year={2016},
}
Yueke Hu. Cuspidal part of an Eisenstein series restricted to an index 2 subfield. 2016. Vol. 2. In Research in Number Theory. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220626173409300224480.
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