Pullback formulas for nearly holomorphic Saito-Kurokawa lifts

• Main Authors: Shih-Yu Chen, 陳昰宇
• Other Authors: 謝銘倫
• Format: Others
• Language: en_US
• Published: 2018
• Online Access: http://ndltd.ncl.edu.tw/handle/ftgedv

博士 === 國立臺灣大學 === 數學研究所 === 106 === We give explicit pullback formulas for nearly holomorphic Saito-Kurokawa lifts restrict to product of upper half-plane against with product of elliptic modular forms. We generalize the formula of Ichino to modular forms of higher level and free the restriction on weights. The explicit formulas provide non-trivial examples for the refined Gross-Prasad conjecture for (SO(5), SO(4)) in the non-tempered cases. As an application, we obtain new cases for Deligne’s conjecture for central critical values of certain automorphic L-functions for GL(3) × GL(2).