Mean values of multivariable multiplicative functions and applications to the average number of cyclic subgroups and multivariable averages associated with the LCM function

2021/08/23 by Driss Essouabri, Essouabri, D., Christoper Salinas Zavala +3
Mathematics · #11M32 #11M41 #11M45 #11N37 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2108.10247

openalex publication_date 2021/08/23 · openalex created_date 2021/08/30 · openalex updated_date 2026/07/28

Abstract

We use multiple zeta functions to prove, under suitable assumptions, precise asymptotic formulas for the averages of multivariable multiplicative functions. As applications, we prove some conjectures on the average number of cyclic subgroups of the group \mathbb Z_m1×…× \mathbb Z_mn and multivariable averages associated with the LCM function.

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