A modified Möbius μ-function

We consider a generalized type of unique factorization of the positive integers with restrictions on the exponents and view them as a family of arithmetic convolutions and divisibility relations, similar to the convolutions defined by Narkewicz [On a class of arithmetical convolutions, Colloq. Math. 10 (1963) 81–94]. We introduce special types of multiplicativity corresponding to these convolutions, and discuss algebraic properties of the associated arithmetic convolutions and analogs of the Möbius functions. We also prove asymptotics for analogs of the totient function, totient summatory function, and divisor summatory function.

show abstract

A generalization of the infinitary divisibility relation: Algebraic and analytic properties

Burnett

Osterman

2019

Int. J. Number Theory

View full text Add to dashboard Cite

show abstract

Arithmetical Functions Associated with the k-ary Divisors of an Integer

Burnett

Grayson

Sullivan

et al. 2018

International Journal of Mathematics and Mathematical Sciences

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

A modified Möbius μ-function

Abstract: We investigate a modified Möbius μ-function which is related to an infinite product of shifted Riemann zeta-functions. We prove conditional and unconditional upper and lower bounds for its summatory function, and, finally, we discuss relations with Riemann's hypothesis.

Cited by 2 publications

References 7 publications

A generalization of the infinitary divisibility relation: Algebraic and analytic properties

A generalization of the infinitary divisibility relation: Algebraic and analytic properties

Arithmetical Functions Associated with the k-ary Divisors of an Integer

Contact Info

Product

Resources

About