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Waldspurger's period integral for newforms

Volume 195 / 2020

Yueke Hu, Jie Shu, Hongbo Yin Acta Arithmetica 195 (2020), 177-197 MSC: Primary 11F70. DOI: 10.4064/aa190212-3-10 Published online: 13 May 2020


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).


  • Yueke HuYau Mathematical Sciences Center
    Tsinghua University
    Beijing 100084, China
  • Jie ShuSchool of Mathematical Sciences
    Tongji University
    Shanghai 200092, China
  • Hongbo YinSchool of Mathematics
    Shandong University
    Jinan, Shandong 250100, China

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