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Miklós Schweitzer
2016 Miklós Schweitzer
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2016 Miklós Schweitzer
Problems
(1)
Completely multiplicative, partial sum ax+O(1)
Source: Miklós Schweitzer 2016, Problem 1
11/2/2016
For which complex numbers
α
\alpha
α
does there exist a completely multiplicative, complex-valued arithmetic function
f
f
f
such that
∑
n
<
x
f
(
n
)
=
α
x
+
O
(
1
)
?
\sum_{n<x}f(n)=\alpha x+O(1)\,\,?
n
<
x
∑
f
(
n
)
=
αx
+
O
(
1
)
?
Analytic Number Theory
number theory
complex numbers