List questions from analytic-number-theory

Published on 25 May 2014 - 2:51

286

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Prove or disprove that $\forall k\in\mathbb N$ there exist three consecutive primes such that $p_i-p_{i-1}\gt k$ and $p_{i+1}-p_{i}\gt k$

Published on 27 May 2014 - 6:42

284

Views

Calculating the class group of $\mathcal{O}_K$, for $K=\mathbb{Q}(\sqrt{7})$?

Published on 28 May 2014 - 1:12

308

Views

Apostol, Introduction to Analytic Number Theory, Chapter 1, Ex. 29

Published on 29 May 2014 - 16:23

45

Views

How to show $\sum_{n\leq x}d(n)=\sum_{ab\leq x}1$?

Published on 25 Mar 2026 - 18:48

526

Views

Is there a formula for Merten's function $M(x)=\sum_{n\leq x}\mu (n)$?

Published on 30 May 2014 - 13:39

111

Views

What am I doing wrong with Möbius inversion?

Published on 25 Mar 2026 - 9:46

90

Views

Confused About Step in Proof of Divergence of $\sum \frac{1}{p}$

Published on 30 Mar 2026 - 13:04

216

Views

How to find an upper bound for $f(n)=\sum_{k=1}^{n}\frac{1}{d^{9}(k)}$?

Published on 31 May 2014 - 0:46

182

Views

How to show $\sum_{d\mid k}\frac{\mu (d)}{d}\left(\log\left(\frac{x}{d}\right)+O(1)\right)=\left(\sum_{d\mid k}\frac{\mu (d)}{d}\right)\log x+O(1)$

Published on 31 May 2014 - 12:54

498

Views

Identities of Hecke operators

Published on 27 Mar 2026 - 21:51

80

Views

Prove that the set has zero density

Published on 02 Jun 2014 - 14:11

301

Views

A set with zero density

Published on 03 Jun 2014 - 7:55

66

Views

bounding gaps between points in an interval

Published on 04 Jun 2014 - 6:44

94

Views

Summation formula in dimension 2

Published on 05 Jun 2014 - 7:14

List Question

What is $\varlimsup \frac{\omega(n)}{\log n}$?

Prove or disprove that $\forall k\in\mathbb N$ there exist three consecutive primes such that $p_i-p_{i-1}\gt k$ and $p_{i+1}-p_{i}\gt k$

Calculating the class group of $\mathcal{O}_K$, for $K=\mathbb{Q}(\sqrt{7})$?

Apostol, Introduction to Analytic Number Theory, Chapter 1, Ex. 29

How to show $\sum_{n\leq x}d(n)=\sum_{ab\leq x}1$?

Is there a formula for Merten's function $M(x)=\sum_{n\leq x}\mu (n)$?

What am I doing wrong with Möbius inversion?

Confused About Step in Proof of Divergence of $\sum \frac{1}{p}$

How to find an upper bound for $f(n)=\sum_{k=1}^{n}\frac{1}{d^{9}(k)}$?

How to show $\sum_{d\mid k}\frac{\mu (d)}{d}\left(\log\left(\frac{x}{d}\right)+O(1)\right)=\left(\sum_{d\mid k}\frac{\mu (d)}{d}\right)\log x+O(1)$

Identities of Hecke operators

Prove that the set has zero density

A set with zero density

bounding gaps between points in an interval

Summation formula in dimension 2

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