On multiplicative functions resembling the Möbius function

Pretentious Multiplicative Functions and an Inequality for the Zeta-Function

We note how several central results in multiplicative number theory may be rephrased naturally in terms of multiplicative functions f that pretend to be another multiplicative function g. We formalize a ‘distance’ which gives a measure of such pretentiousness, and as one consequence obtain a curious inequality for the zeta-function. A common theme in several problems in multiplicative number th...

A weighted Möbius function

Computing the Summation of the Möbius Function

On a Multiplicative Partition Function

Let D(s) = ∑∞ m=1 amm −s be the Dirichlet series generated by the infinite product ∏∞ k=2(1− k−s). The value of am for squarefree integers m with n prime factors depends only on the number n, and we let f(n) denote this value. We prove an asymptotic estimate for f(n) which allows us to solve several problems raised in a recent paper by M. V. Subbarao and A. Verma.

On the Möbius Function of Permutations with One Descent

The set of all permutations, ordered by pattern containment, is a poset. We give a formula for the Möbius function of intervals [1, π] in this poset, for any permutation π with at most one descent. We compute the Möbius function as a function of the number and positions of pairs of consecutive letters in π that are consecutive in value. As a result of this we show that the Möbius function is un...