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Results tagged with arithmetic-functions
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user 307675
An arithmetic function is one whose domain is the positive integers and whose range is a subset of the complex numbers. There are a number of important number-theoretic examples.
6
votes
Approximation of partial sum over prime omega function
By partial summation, one has
$$
S(N) = N\sum_{n=1}^N \omega(n) - \int_{1}^N \bigg(\sum_{n\leq t} \omega(n)\bigg) dt.
$$
Using Mertens' theorem with the classical error term in the prime number theore …
- 1,990
2
votes
Brun-Titchmarsh for sum over square divisors
I realized this is actually pretty much the same problem as one arising when studying squarefree numbers in short intervals. Using some results from Filaseta and Trifonov [1] (specifically the estimat …
- 1,990
3
votes
1
answer
171
views
Brun-Titchmarsh for sum over square divisors
Let $f(n)$ be a nonnegative arithmetic function satisfying
$f(p^l) \leq A_1^l$ for all primes $p$, integers $l\geq 1$, and some constant $A_1$;
$f(n) \leq A_2 n^\varepsilon$ for all $\varepsilon > 0$ …
- 1,990
4
votes
0
answers
80
views
Joint mean values of arithmetic functions in sequences and families of sequences
This is a bit of a follow up question to this question I asked a couple days ago. The main content of that post can be phrased as asking for a nontrivial lower bound on the sum
$$
\sum_{n\leq x} \Lamb …
- 1,990