Mean Values of Arithmetic Functions under Congruences with the Euler Function
نویسندگان
چکیده
منابع مشابه
Arithmetic Functions and the Euler Phi Function
• An arithmetic function takes positive integers as inputs and produces real or complex numbers as outputs. • If f is an arithmetic function, the divisor sum Df(n) is the sum of the values of f at the positive divisors of n. • τ (n) is the number of positive divisors of n; σ(n) is the sum of the positive divisors of n. • The Möbius function μ(n) is 1 if n = 1 and 0 if n has a repeated prime fac...
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Let f(n) be a totally multiplicative function such that |f(n)| ≤ 1 for all n, and let F (s) = ∑∞ n=1 f(n)n−s be the associated Dirichlet series. A variant of Halász’s method is developed, by means of which estimates for ∑N n=1 f(n)/n are obtained in terms of the size of |F (s)| for s near 1 with 1. The result obtained has a number of consequences, particularly concerning the zeros of the p...
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ژورنال
عنوان ژورنال: Turkish Journal of Analysis and Number Theory
سال: 2020
ISSN: 2333-1100
DOI: 10.12691/tjant-8-2-4