User Rob

13 votes

3 answers

4k views

Non-increasing sequence of positive real numbers with prime index

asked Oct 16, 2011 at 1:23

13 votes

1 answer

2k views

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

asked Dec 10, 2011 at 5:46

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?

asked Sep 23, 2011 at 0:41

8 votes

1 answer

594 views

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

asked Sep 29, 2011 at 2:58

7 votes

2 answers

431 views

Mean value of arithmetic function

asked Oct 1, 2011 at 8:23

7 votes

1 answer

520 views

How will this equation imply PNT

asked Oct 16, 2011 at 5:18

6 votes

1 answer

212 views

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

asked Sep 22, 2011 at 7:07

6 votes

1 answer

404 views

How to prove this combinatorial identity?

asked Sep 7, 2012 at 8:12

5 votes

2 answers

1k views

Method of image charge for ellipse

asked May 29, 2012 at 15:13

5 votes

0 answers

191 views

Euler summation and its transformation

asked Sep 5, 2011 at 22:15

5 votes

1 answer

262 views

Express Dirichlet series in terms of Dirichlet L-function

asked Oct 28, 2011 at 1:28

5 votes

2 answers

210 views

Farey fractions in arithmetic progression

asked Oct 30, 2011 at 3:14

5 votes

1 answer

129 views

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

asked Nov 1, 2011 at 2:55

5 votes

2 answers

1k views

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

asked Nov 3, 2011 at 1:29

4 votes

1 answer

233 views

Relation between zeta function and Dirichlet L-function

asked Dec 10, 2011 at 19:32

4 votes

2 answers

301 views

How to prove this inequality using prime number theorem

asked Oct 1, 2011 at 8:16

4 votes

2 answers

2k views

Laplace transform of a Gaussian function with complex variable

asked Aug 17, 2012 at 20:35

4 votes

2 answers

163 views

Find the radius of convergence for this series

asked Dec 12, 2011 at 4:05

3 votes

2 answers

2k views

Real Dirichlet characters mod $k$

asked Dec 13, 2011 at 2:39

3 votes

0 answers

77 views

signature function of Weyl group element in LieArt

asked Jun 25, 2015 at 19:40

3 votes

3 answers

300 views

Convergence of prime series

asked Sep 27, 2011 at 8:01

3 votes

2 answers

241 views

Will partial summation work for this problem?

asked Sep 28, 2011 at 4:28

3 votes

0 answers

175 views

Subadditive in analytic number theory

asked Sep 11, 2011 at 21:08

3 votes

1 answer

345 views

Dirichlet character over Riemann zeta function

asked Dec 11, 2011 at 8:25

3 votes

0 answers

391 views

Dirichlet series represents an analytic function

asked Dec 10, 2011 at 17:53

2 votes

2 answers

251 views

A question about an identity involving Dirichlet characters

asked Nov 5, 2011 at 3:17

2 votes

1 answer

693 views

the volume of 3-sphere

asked Apr 12, 2011 at 21:14

2 votes

0 answers

82 views

the nth power Logarithmic Integral [duplicate]

asked Sep 24, 2011 at 6:39

2 votes

1 answer

543 views

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

asked Sep 25, 2011 at 3:09

2 votes

1 answer

662 views

What is the dual lattice of Kagome lattice?

asked Feb 10, 2014 at 1:13

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50 Questions

Non-increasing sequence of positive real numbers with prime index

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

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?

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

Mean value of arithmetic function

How will this equation imply PNT

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

How to prove this combinatorial identity?

Method of image charge for ellipse

Euler summation and its transformation

Express Dirichlet series in terms of Dirichlet L-function

Farey fractions in arithmetic progression

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

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

Relation between zeta function and Dirichlet L-function

How to prove this inequality using prime number theorem

Laplace transform of a Gaussian function with complex variable

Find the radius of convergence for this series

Real Dirichlet characters mod $k$

signature function of Weyl group element in LieArt

Convergence of prime series

Will partial summation work for this problem?

Subadditive in analytic number theory

Dirichlet character over Riemann zeta function

Dirichlet series represents an analytic function

A question about an identity involving Dirichlet characters

the volume of 3-sphere

the nth power Logarithmic Integral [duplicate]

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

What is the dual lattice of Kagome lattice?