Waldspurger's period integral for newforms

Yueke Hu Yau Mathematical Sciences Center, Tsinghua University, Beijing 100084, China Jie Shu School of Mathematical Sciences, Tongji University, Shanghai 200092, China Hongbo Yin School of Mathematics, Shandong University, Jinan, Shandong 250100, China

Number Theory mathscidoc:2206.24012

Acta Arithmetica, 195, (2), 177-197, 2020.5
We discuss Waldspurger’s local period integral for newforms in new cases. The main tool is the work of Hu and Nelson (2018) on Waldspurger’s period integral using minimal vectors, and the explicit relation between newforms and minimal vectors. We use a representation-theoretical trick to simplify computations for newforms. As an example, we compute the local integral coming from a special arithmetic setting which was used to study the 3-part full BSD conjecture by Hu et al. (2019).
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  title={Waldspurger's period integral for newforms},
  author={Yueke Hu, Jie Shu, and Hongbo Yin},
  booktitle={Acta Arithmetica},
Yueke Hu, Jie Shu, and Hongbo Yin. Waldspurger's period integral for newforms. 2020. Vol. 195. In Acta Arithmetica. pp.177-197. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220629150850673325488.
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