学术报告报告主题: Artin’s primitive root conjecture and the index of the reductions of algebraic numbers
报 告 人: Pietro Sgobba 助理教授（西安交通利物浦大学）
报告时间：2024年1月18日（星期四）上午10:00-11:00
报告地点: 37号楼3A01
邀 请 人: 胡甦副教授
欢迎广大师生前往！
数学学院
2024年 1月12日
报告摘要：Artin’s primitive root conjecture (1927) states that given an integer a which is neither 0,1,-1, nor a perfect square, there are infinitely many primes p such that a is a primitive root modulo p. We consider a more general question over number fields. Let K be a number field and let a be a nonzero algebraic number in K. For all but finitely many primes p of K, the reduction (a mod p) is well-defined, and we may consider its multiplicative index. Assuming the Generalized Riemann Hypothesis, we then study the natural density of primes of K for which this index lies in a given set of positive integers, and we focus on the case where this set is defined by prescribing valuations for its elements. The obtained results hold unconditionally under certain conditions. Part of the work is joint with Järviniemi, Perucca and Moree.
报告人介绍：Pietro Sgobba obtained his PhD at the University of Luxembourg in 2022 under the supervision of Antonella Perucca. He was then a postdoc at the University of Luxembourg and since September 2023 he is an assistant professor at Xi'an Jiaotong-Liverpool University in Suzhou, China. His main interests lie in algebraic and analytic number theory.