z-logo
open-access-imgOpen Access
Converegence of a series leading to an analogue of Ramanujan's assertion on squarefree integers
Author(s) -
G. Sudhaamsh Mohan Reddy,
S. Srinivas Rau,
B. Uma
Publication year - 2018
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.v38i2.34878
Subject(s) - mathematics , square free integer , ramanujan's sum , assertion , combinatorics , prime (order theory) , series (stratigraphy) , discrete mathematics , computer science , programming language , paleontology , biology
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).

The content you want is available to Zendy users.

Already have an account? Click here to sign in.
Having issues? You can contact us here