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Reddy, G. Sudhaamsh Mohan; Rau, S Srinivas; Uma, B.
Boletim da Sociedade Paranaense de Matemática, 02/2018, Volume: 38, Issue: 2Journal Article
Let d be a squarefree integer. We prove that(i) Pnμ(n)nd(n′) converges to zero, where n′ is the product of prime divisors of nwith ( dn ) = +1. We use the Prime Number Theorem.(ii) Q( dp )=+1(1 −1ps ) is not analytic at s=1, nor is Q( dp )=−1(1 −1ps ) .(iii) The convergence (i) leads to a proof that asymptotically half the squarefree ideals have an even number of prime ideal factors (analogue of Ramanujan’s assertion).
