DELIGNE'S CONJECTURE AND THE CROSS-RATIO FORMULA
陳昰宇助理教授國立清華大學數學系 15:30–17:00 鴻經館M107Abstract：
At the 1977 Corvallis conference, P.Deligne proposed a remarkable conjecture describing the algebraicity of critical L-values in terms of motivic periods. The conjecture has recently been settled for pure motives of rank one. In all other known cases in the literature, proofs typically depend on integral representations of the relevant L-functions. In the framework of the Langlands–Clozel correspondence, we introduce, on the automorphic side, a cross-ratio formula for the critical values of Rankin–Selberg L-functions. This formula provides a new method for addressing Deligne’s conjecture. In this talk, we will introduce Deligne’s conjecture and present the cross-ratio formula. If time permits, we will also outline a proof of Deligne’s conjecture for the symmetric power L-functions of modular forms.