A Menon-type Identity with Multiplicative and Additive Characters

作者：Li, Yan^*; Hu, Xiaoyu; Kim, Daeyeoul

来源：Taiwanese Journal of Mathematics, 2019, 23(3): 545-555.

DOI：10.11650/tjm/180702

• Menon's identity
• Dirichlet character
• additive character
• divisor function
• Euler's totient function
• Iverson bracket
• Chinese remainder theorem

This paper studies Menon-type identities involving both multiplicative characters and additive characters. In the paper, we shall give the explicit formula of the following sum
Sigma gcd(a - 1, b(1), ..., b(k), n) chi(a)lambda(1)(b(1)) ... lambda(k) (b(k)),
a is an element of Z(n)*
b(1), ..., b(k)is an element of Z(n)
Where for a positive integer n, Z(n)* is the group of units of the ring Z(n) = Z/nZ, gcd represents the greatest common divisor, chi is a Dirichlet character modulo n, and for nonnegative integer k, lambda(1),..., lambda(k) are additive characters of Z(n). Our formula further extends the previous results by Sury [13], Zhao-Cao [17] and Li-Hu-Kim [4].

• 出版日期2019-6
• 单位中国农业大学