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VOL. 84 | 2020 On mean values of multivariable complex valued multiplicative functions and applications
Driss Essouabri

Editor(s) Hidehiko Mishou, Takashi Nakamura, Masatoshi Suzuki, Yumiko Umegaki

Abstract

We study the asymptotic behavior of a density function $$ t \to N(f; \mathcal{N}; t) = \sum_{\{\mathbf{m}=(m_1, \dots, m_n) \in \mathbb{N}^n; \mathcal{N}(\mathbf{m}) \leq t\}} f(m_1, \dots, m_n) $$ when $f:\mathbb{N}^n \rightarrow \mathbb{C}$ is a suitable multivariable complex valued multiplicative function, and the family of generalized balls $\{\mathcal{N} \le t\} \cap [0, \infty)^n$ are determined by a positive definite form on $[0, \infty)^n$. Several arithmetic applications of this work are given.

Information

Published: 1 January 2020
First available in Project Euclid: 27 May 2020

zbMATH: 07283180

Digital Object Identifier: 10.2969/aspm/08410023

Subjects:
Primary: 11M32, 11M41, 11N37, 11P21

Rights: Copyright © 2020 Mathematical Society of Japan

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