鱼虾蟹游戏

题    目：Explicit bounds of generalized incomplete Gauss sums and applications in order-optimal           sequence design

主讲人：刘华宁 教授

单    位：西北大学

时    间：2025年12月26日 11:00

地    点：鱼虾蟹游戏 207教室

摘    要：Generalized incomplete Gauss sums play a central role in bridging number theory with            communication, radar, and integrated sensing systems. However, their practical use has been               hindered for decades by the absence of tight explicit bounds. This talk resolves this long-standing      challenge by establishing the first explicit and tight upper bound for generalized incomplete Gauss     sums. Our analysis refines Paris’ asymptotic expansion through a tailored error-control strategy for complementary error functions and leverages the fast convergence of the Fibonacci zeta function.      Building on this explicit bound, we construct five families of order-optimal sequence sets, including    three Chu-sequence-derived sets ($C_1$ for low correlation, $C_2$ and $C_3$ for low ambiguity) and two Alltop-sequence-derived sets $A_1$ and $A_2$. Notably, the Alltop-based set $A_2$ achieves, for the first time, simultaneous optimality in both wide low-ambiguity region and low aperiodic                  correlation, shattering the long-standing trade-off between these two critical performance metrics in existing sequence designs. This is a joint work with Zilong Liu. 

简    介：刘华宁，西北大学数学鱼虾蟹游戏 教授、博士生导师，剑桥大学与山东大学博士后。目前担任《纯粹数学与应用数学》期刊执行编委。研究方向为解析数论及其应用，发表论文100余篇。先后主持多项国家自然科学基金和1项陕西省杰出青年基金项目，曾获得钟家庆数学奖、全国优秀博士学位论文提名、霍英东教育基金会青年教师奖、陕西省青年科技新星以及两项陕西省科学技术奖。