p-adic L-functions and modifying factors
报告专家：孙斌勇 院士（浙江大学数学高等研究院&新基石科学实验室）
报告时间：10月20日（周二）下午16:00-17:00
报告地点：国家天元数学西南中心516
报告摘要：
The Riemann zeta function ζ(s) takes rational values at negative odd integers, and the Kummer congruence relations assert that these values satisfy congruences enabling them to be interpolated continuously in the p-adic topology. The p-adic L-function of Kubota-Leopoldt serves as the p-adic analog of the Riemann zeta function, incorporating the Kummer congruence relations. Coates conjectured that there exist p-adic L-functions attached to motives or algebraic automorphic representations, which interpolate the critical values of complex L-functions with explicit modifying factors at infinity and at p. Starting with basic notions on p-adic L-functions, we will discuss Coates' conjecture in the setting of automorphic representations. We verify it for symplectic-type representations. The talk is based on a joint work with Dongwen Liu.
专家简介：
孙斌勇，中国科学院院士，浙江大学数学高等研究院教授、博士生导师。研究方向为李群表示与自守形式。曾获2014年陈嘉庚青年科学奖、2016年中国优秀青年科技人才奖、2016年中国科学院青年科学家奖、2018年国家自然科学奖二等奖、2020年全国争先创新奖等。受邀在2022年国际数学家大会作45分钟报告。
邀请人：连增
