Waldspurger's period integral for newforms

2019/07/26 by Hu, Yueke, Shu, Jie, Yin, Hongbo
#FOS: Mathematics #Number Theory (math.NT) #[2010]{Primary 11F70}

paper · doi:10.48550/arxiv.1907.11428

Abstract

In this paper we discuss Waldspurger's local period integral for newforms in new cases. The main ingredient is the work \citeHN18 on Waldspurger's period integral using the minimal vectors, and the explicit relation between the newforms and the 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 3-part full BSD conjecture in \citeHSY.

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