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A note on the congruent distribution of the number of prime factors of natural numbers
Published online by Cambridge University Press: 22 January 2016
Abstract
Let n = p1p2 … pr be a product of r prime numbers which are not necessarily different. We define then an arithmetic function µm(n) by
where m is a natural number. We further define the function L(s, µm) by the Dirichlet series
and will show that L(s, µm), (m ≥ 3), has an infinitely many valued analytic continuation into the half plane Re s > ½.
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- Research Article
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- Copyright © Editorial Board of Nagoya Mathematical Journal 2001
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