Exercise 8.3. Let c(n) denote Ramanujan's sum and let M(r)=En
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
Problem 17EQ
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![Exercise 8.3. Let c(n) denote Ramanujan's sum and let M(r) = En<++(n), the partial
sums of the Möbius function.
(a) Prove that
[alm) – EdM ().
TL
LCa (m)
k=1
In particular, when n = m, we have
Ca (m) =dM (G
d|m
(b) Use (a) to deduce that
H(m/d) Cx(d).
M(m) =
P
k=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F16d5ab89-cae5-4d80-b8cc-2688a1c981a8%2Fd986b973-6393-4ef3-8154-6537729684ac%2Fxcpnc3d_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 8.3. Let c(n) denote Ramanujan's sum and let M(r) = En<++(n), the partial
sums of the Möbius function.
(a) Prove that
[alm) – EdM ().
TL
LCa (m)
k=1
In particular, when n = m, we have
Ca (m) =dM (G
d|m
(b) Use (a) to deduce that
H(m/d) Cx(d).
M(m) =
P
k=1
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