Question

If $|a-b| \geq \sqrt{N}$ for every $a \neq b \in \text{supp}(\hat{f})$, what can we say about $f : \mathbb{Z}/N\mathbb{Z} \to \mathbb{C}?$

score 81 · Answer 1 · 2026-04-02 15:04:40

81

Views

If $|a-b| \geq \sqrt{N}$ for every $a \neq b \in \text{supp}(\hat{f})$, what can we say about $f : \mathbb{Z}/N\mathbb{Z} \to \mathbb{C}?$

Published on 02 Apr 2026 - 15:04

score 218 · Answer 2 · 2016-09-14 23:10:55

218

Views

Is $e^{2\pi i m/k}$ a $k$th root of unity even if $\gcd (m,k)>1$?

Published on 14 Sep 2016 - 23:10

score 358 · Answer 3 · 2026-03-29 12:30:12

358

Views

Heisenberg's inequality for the Fourier transform on finite fields

Published on 29 Mar 2026 - 12:30

score 48 · Answer 4 · 2016-09-16 03:38:25

48

Views

Lemma 11.22 in Iwaniec-Kowalski

Published on 16 Sep 2016 - 3:38

score 331 · Answer 5 · 2026-04-02 00:42:52

331

Views

Does $\sum_{n = 2}^{\infty} [\zeta(n) - 1]$ converge?

Published on 02 Apr 2026 - 0:42

score 105 · Answer 6 · 2026-03-25 19:07:07

105

Views

Calculate $\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^T\frac{\zeta(\frac{3}{2}+it)}{\zeta(\frac{3}{2}-it)}dt$ as $\sum_{n=1}^\infty\frac{\mu(n)}{n^3}$

Published on 25 Mar 2026 - 19:07

score 147 · Answer 7 · 2026-03-28 01:07:19

147

Views

What is the close form of the sum of reciprocals of $k!$, $k!!$, and so on? Moreover, is it transcendental?

Published on 28 Mar 2026 - 1:07

score 747 · Answer 8 · 2026-03-25 14:20:59

747

Views

Dirichlet hyperbola methods : estimate functions # of ordered pairs

Published on 25 Mar 2026 - 14:20

score 262 · Answer 9 · 2016-09-21 18:11:47

262

Views

Estimate sum of certain arithmetic functions

Published on 21 Sep 2016 - 18:11

score 145 · Answer 10 · 2016-09-25 17:46:44

145

Views

Theorem $8.12$ Apostol's Analytic Number Theory?

Published on 25 Sep 2016 - 17:46

score 92 · Answer 11 · 2016-09-25 19:46:07

92

Views

Prove that $a = b^m$ if $\frac{a^n-1}{b^n-1} \in \mathbb{Z}$ for $n \in \mathbb{N}.$

Published on 25 Sep 2016 - 19:46

score 59 · Answer 12 · 2026-04-04 07:33:39

59

Views

Prove $(n|p) = \chi (n)$ for $p$ a prime.

Published on 04 Apr 2026 - 7:33

score 162 · Answer 13 · 2016-09-27 12:37:19

162

Views

Is there a Ramanujan's sum function with real argument?

Published on 27 Sep 2016 - 12:37

score 82 · Answer 14 · 2016-09-29 23:49:41

82

Views

Why does this integral converge for all $s \in \mathbb C$?

Published on 29 Sep 2016 - 23:49

score 631 · Answer 15 · 2016-10-02 00:05:00

631

Views

Does the Riemann zeta function converge in higher dimensions?

Published on 02 Oct 2016 - 0:05

List Question

If $|a-b| \geq \sqrt{N}$ for every $a \neq b \in \text{supp}(\hat{f})$, what can we say about $f : \mathbb{Z}/N\mathbb{Z} \to \mathbb{C}?$

Is $e^{2\pi i m/k}$ a $k$th root of unity even if $\gcd (m,k)>1$?

Heisenberg's inequality for the Fourier transform on finite fields

Lemma 11.22 in Iwaniec-Kowalski

Does $\sum_{n = 2}^{\infty} [\zeta(n) - 1]$ converge?

Calculate $\lim_{T\to\infty}\frac{1}{2T}\int_{-T}^T\frac{\zeta(\frac{3}{2}+it)}{\zeta(\frac{3}{2}-it)}dt$ as $\sum_{n=1}^\infty\frac{\mu(n)}{n^3}$

What is the close form of the sum of reciprocals of $k!$, $k!!$, and so on? Moreover, is it transcendental?

Dirichlet hyperbola methods : estimate functions # of ordered pairs

Estimate sum of certain arithmetic functions

Theorem $8.12$ Apostol's Analytic Number Theory?

Prove that $a = b^m$ if $\frac{a^n-1}{b^n-1} \in \mathbb{Z}$ for $n \in \mathbb{N}.$

Prove $(n|p) = \chi (n)$ for $p$ a prime.

Is there a Ramanujan's sum function with real argument?

Why does this integral converge for all $s \in \mathbb C$?

Does the Riemann zeta function converge in higher dimensions?

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