An equidistribution theorem for holomorphic siegel modular forms for GSP4 and its applications

Henry H. Kim, Satoshi Wakatsuki, Takuya Yamauchi

研究成果: Article査読

2 被引用数 (Scopus)


We prove an equidistribution theorem for a family of holomorphic Siegel cusp forms for in various aspects. A main tool is Arthur's invariant trace formula. While Shin [Automorphic Plancherel density theorem, Israel J. Math.192(1) (2012), 83-120] and Shin-Templier [Sato-Tate theorem for families and low-lying zeros of automorphic -functions, Invent. Math.203(1) (2016) 1-177] used Euler-Poincaré functions at infinity in the formula, we use a pseudo-coefficient of a holomorphic discrete series to extract holomorphic Siegel cusp forms. Then the non-semisimple contributions arise from the geometric side, and this provides new second main terms in Theorem 1.1 which have not been studied and a mysterious second term also appears in the second main term coming from the semisimple elements. Furthermore our explicit study enables us to treat more general aspects in the weight. We also give several applications including the vertical Sato-Tate theorem, the unboundedness of Hecke fields and low-lying zeros for degree 4 spinor -functions and degree 5 standard -functions of holomorphic Siegel cusp forms.

ジャーナルJournal of the Institute of Mathematics of Jussieu
出版ステータスPublished - 2020 3 1

ASJC Scopus subject areas

  • 数学 (全般)


「An equidistribution theorem for holomorphic siegel modular forms for GSP<sub>4</sub> and its applications」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。