On the Waldspurger Formula and the Metaplectic Ramanujan Conjecture over Number Fields

2018/08/16 by Jingsong Chai, Chai, Jingsong, Zhi Qi +1
Mathematics · #11F37 #11F67 #11F70 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1808.05398

openalex publication_date 2018/08/16 · openalex created_date 2018/08/22 · openalex updated_date 2026/07/28

Abstract

In this paper, by inputting the Bessel identities over the complex field in previous work of the authors, the Waldspurger formula of Baruch and Mao is extended from totally real fields to arbitrary number fields. This is applied to give a non-trivial bound towards the Ramanujan conjecture for automorphic forms of the metaplectic group \widetildeSL₂ for the first time in the generality of arbitrary number fields.

Citations

• On Modular Forms of Half Integral Weight

Related

• Arthur packets for metaplectic groups
• The Shimura-Waldspurger correspondence for Mp(2n)
• Whittaker functions on metaplectic covers of GL(r)
• The Whittaker period formula on Metaplectic SL(2)
• On the Ramanujan conjecture over number fields