The MathNet Korea
Information Center for Mathematical Science

세미나

Information Center for Mathematical Science

세미나

한국고등과학원 세미나
Title Equidistribution theorems for holomorphic Siegel cusp forms
Date 2018-12-18
Speaker Kim, Henry(Univ. of Toronto)
Sponsors 2018-12-18
Host KIAS
Place 1423
Abstract We explain equidistribution theorems for a family of holomorphic Siegel cusp forms of GSp_4 in the level and weight aspects. A main tool is Arthur's invariant trace formula. While Shin-Templier used Euler-Poincare functions at the infinity in the formula, we use pseudo-coefficients of holomorphic discrete series to extract only holomorphic Siegel cusp forms. Then the non-semisimple contributions arise from the geometric side, and this provides new second main terms which have not been studied, and which correspond to endoscopic cuspidal representations with large discrete series at the infinity. We give several applications, including the vertical Sato-Tate theorem and low-lying zeros for degree 4 spinor L-functions and degree 5 standard L-functions of holomorphic Siegel cusp forms. This is a joint work with Satoshi Wakatsuki and Takuya Yamauchi. If time permits, we explain work in progress to the generalization to Sp_{2n}.