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Rob
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13 votes
3 answers
4k views

Non-increasing sequence of positive real numbers with prime index

13 votes
1 answer
2k views

Mean Value of a Multiplicative Function close to $n$ in Terms of the Zeta Function

10 votes
1 answer
1k views

How do I prove $\sum_{n \leq x} \frac{\mu (n)}{n} \log^2{\frac{x}{n}}=2\log{x}+O(1)$? Can I use Abel summation?

8 votes
1 answer
569 views

Showing that $\sum_{n \leq x} \frac{\mu(n)}{n} \log \frac{x}{n} = O(1)$.

7 votes
2 answers
405 views

Mean value of arithmetic function

7 votes
1 answer
474 views

How will this equation imply PNT

6 votes
1 answer
209 views

Estimating $\int_e^x \log\log{t}\, dt$ so the error term in within $O\left(\frac{x}{\log^2{x}}\right)$

6 votes
1 answer
400 views

How to prove this combinatorial identity?

5 votes
2 answers
957 views

Method of image charge for ellipse

5 votes
0 answers
187 views

Euler summation and its transformation

5 votes
1 answer
253 views

Express Dirichlet series in terms of Dirichlet L-function

5 votes
2 answers
207 views

Farey fractions in arithmetic progression

5 votes
1 answer
129 views

Counting the solutions of $x^2 \equiv y^2-d \pmod p$

5 votes
2 answers
1k views

A question about the proof that $(\mathbb{Z}/p\mathbb{Z})^\times$ is cyclic

4 votes
1 answer
227 views

Relation between zeta function and Dirichlet L-function

4 votes
2 answers
288 views

How to prove this inequality using prime number theorem

4 votes
2 answers
2k views

Laplace transform of a Gaussian function with complex variable

4 votes
2 answers
163 views

Find the radius of convergence for this series

3 votes
2 answers
2k views

Real Dirichlet characters mod $k$

3 votes
0 answers
73 views

signature function of Weyl group element in LieArt

3 votes
3 answers
289 views

Convergence of prime series

3 votes
2 answers
237 views

Will partial summation work for this problem?

3 votes
0 answers
174 views

Subadditive in analytic number theory

3 votes
1 answer
331 views

Dirichlet character over Riemann zeta function

3 votes
0 answers
356 views

Dirichlet series represents an analytic function

2 votes
2 answers
246 views

A question about an identity involving Dirichlet characters

2 votes
1 answer
618 views

the volume of 3-sphere

2 votes
0 answers
81 views

the nth power Logarithmic Integral [duplicate]

2 votes
1 answer
511 views

Exercise I.1.6 from Tenenbaum's "Introduction to analytic and probabilistic number theory"

2 votes
1 answer
587 views

What is the dual lattice of Kagome lattice?