Simplicial Complexes Associated to Certain Subsets of Natural Numbers and Its Applications to Multiplicative Functions
نویسنده
چکیده
We call a set of positive integers closed under taking unitary divisors an unitary ideal. It can be regarded as a simplicial complex. Moreover, a multiplicative arithmetical function on such a set corresponds to a function on the simplicial complex with the property that the value on a face is the product of the values at the vertices of that face. We use this observation to solve the following problems: A. Let r be a positive integer and c a real number. What is the maximum value that ∑
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