报告题目：The theory of vanishing sums and its applications on generalized Bent Functions and Butson Matrices

报告人：Ka Hin Leung，National Univerity of Singapore

报告时间： 4月27日，上午10:00-11:00, 

报告地点：数院新楼308

摘要：

Suppose x_1,..., x_n are roots of unity; and a_1,..., a_n are integers. We say the formal sum a_1x_1 +...+a_n x_n is a vanishing sum if a_1x_1 +...+a_n x_n = 0 in C. I first studied the theory of vanishing sums in [1]. Among all the results in [1], it turns out that many researchers mainly interested in the number \sum|a_i|. However, the structure of the vanishing sums found in [1] did not seem to receive much attention.

In this talk, I will illustrate how the structure of vanishing sums be applied to solve problems on generalized bent functions and Butson matrices. Indeed, I expect the theory can be applied to study many other similar combinatoric objects.

Reference

[1] T.Y. Lam and K.H. Leung, On vanishing sums of roots of unity, J. Algebra, 224 (1), 91-109, 2000.

[2] KH Leung, Q Wang, New nonexistence results on (m, n)-generalized bent functions, Designs, Codes and Crytography 88(4) 755-770, 2020.

[3] KH Leung, Shuxing Li, Songtao Mao, Nonexistence results of generalized bent functions from Z_2^n to Z^m, JCTA, (198), 2023.

[4] JH Chun, KH Leung, M Zhao, On vanishing sums and cyclic Butson matrices 1, Designs Codes and Cryptography 93 (12): 5143-5157,2025