User Rob

13 votes

3 answers

4k views

Non-increasing sequence of positive real numbers with prime index

sequences-and-series analytic-number-theory

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?

asymptotics analytic-number-theory

asked Sep 23, 2011 at 0:41

8 votes

1 answer

569 views

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

number-theory analytic-number-theory

asked Sep 29, 2011 at 2:58

7 votes

2 answers

405 views

Mean value of arithmetic function

analytic-number-theory

asked Oct 1, 2011 at 8:23

7 votes

1 answer

474 views

How will this equation imply PNT

analytic-number-theory

asked Oct 16, 2011 at 5:18

6 votes

1 answer

209 views

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

analysis integration asymptotics

asked Sep 22, 2011 at 7:07

6 votes

1 answer

400 views

How to prove this combinatorial identity?

combinatorics probability-distributions

asked Sep 7, 2012 at 8:12

5 votes

2 answers

957 views

Method of image charge for ellipse

physics

asked May 29, 2012 at 15:13

5 votes

0 answers

187 views

Euler summation and its transformation

analytic-number-theory

asked Sep 5, 2011 at 22:15

5 votes

1 answer

253 views

Express Dirichlet series in terms of Dirichlet L-function

analytic-number-theory

asked Oct 28, 2011 at 1:28

5 votes

2 answers

207 views

Farey fractions in arithmetic progression

analytic-number-theory additive-combinatorics

asked Oct 30, 2011 at 3:14

5 votes

1 answer

129 views

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

elementary-number-theory

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

abstract-algebra elementary-number-theory

asked Nov 3, 2011 at 1:29

4 votes

1 answer

227 views

Relation between zeta function and Dirichlet L-function

analytic-number-theory dirichlet-series

asked Dec 10, 2011 at 19:32

4 votes

2 answers

288 views

How to prove this inequality using prime number theorem

prime-numbers analytic-number-theory

asked Oct 1, 2011 at 8:16

4 votes

2 answers

2k views

Laplace transform of a Gaussian function with complex variable

laplace-transform

asked Aug 17, 2012 at 20:35

4 votes

2 answers

163 views

Find the radius of convergence for this series

sequences-and-series analytic-number-theory

asked Dec 12, 2011 at 4:05

3 votes

2 answers

2k views

Real Dirichlet characters mod $k$

analytic-number-theory

asked Dec 13, 2011 at 2:39

3 votes

0 answers

73 views

signature function of Weyl group element in LieArt

lie-groups lie-algebras computer-algebra-systems

asked Jun 25, 2015 at 19:40

3 votes

3 answers

289 views

Convergence of prime series

reference-request prime-numbers convergence-divergence analytic-number-theory

asked Sep 27, 2011 at 8:01

3 votes

2 answers

237 views

Will partial summation work for this problem?

analytic-number-theory

asked Sep 28, 2011 at 4:28

3 votes

0 answers

174 views

Subadditive in analytic number theory

analytic-number-theory

asked Sep 11, 2011 at 21:08

3 votes

1 answer

331 views

Dirichlet character over Riemann zeta function

analytic-number-theory riemann-zeta dirichlet-series

asked Dec 11, 2011 at 8:25

3 votes

0 answers

356 views

Dirichlet series represents an analytic function

analytic-number-theory dirichlet-series

asked Dec 10, 2011 at 17:53

2 votes

2 answers

246 views

A question about an identity involving Dirichlet characters

analytic-number-theory dirichlet-series

asked Nov 5, 2011 at 3:17

2 votes

1 answer

618 views

the volume of 3-sphere

representation-theory lie-groups

asked Apr 12, 2011 at 21:14

2 votes

0 answers

81 views

the nth power Logarithmic Integral [duplicate]

analysis asymptotics

asked Sep 24, 2011 at 6:39

2 votes

1 answer

511 views

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

analytic-number-theory

asked Sep 25, 2011 at 3:09

2 votes

1 answer

587 views

What is the dual lattice of Kagome lattice?

tiling tessellations lattices-in-lie-groups

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?