Journal of the Ramanujan Mathematical Society

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Multiplicative Functions from Riemann Zeta Function Products


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1 21, Wurruk Avenue, Preston, 3072, Victoria, Australia
     

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In interpreting recent Euler products we are led to theorems concerning the multiplicative function w(m,k) = ∏(1/1-pi-m ai) with k = ∏ piai

For this, we give three related generation functions and show also it is related to various weighted summations over particular factorizations of positive integer k.


Keywords

10K20 Arithmetic Functions (Primary Classification) 30B50, 40A20, 40A30, 10J25, 10H05, 05A19, 10A50.
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  • Multiplicative Functions from Riemann Zeta Function Products

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Authors

Geoffrey B. Campbell
21, Wurruk Avenue, Preston, 3072, Victoria, Australia

Abstract


In interpreting recent Euler products we are led to theorems concerning the multiplicative function w(m,k) = ∏(1/1-pi-m ai) with k = ∏ piai

For this, we give three related generation functions and show also it is related to various weighted summations over particular factorizations of positive integer k.


Keywords


10K20 Arithmetic Functions (Primary Classification) 30B50, 40A20, 40A30, 10J25, 10H05, 05A19, 10A50.