Question

There are infinitely many non-harshad Fibonacci numbers

score 119 · Answer 1 · 2026-03-28 10:04:41

119

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There are infinitely many non-harshad Fibonacci numbers

Published on 28 Mar 2026 - 10:04

score 106 · Answer 2 · 2026-04-05 00:06:31

106

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$\chi(n)=\frac{\tau_k(\chi)}{\sqrt k}\sum_{m=1}^k \bar\chi(m)e^{-\frac{2\pi imn}{k}}$

Published on 05 Apr 2026 - 0:06

score 112 · Answer 3 · 2026-03-28 08:47:52

112

Views

Modular functions and modular forms

Published on 28 Mar 2026 - 8:47

score 131 · Answer 4 · 2026-04-04 17:32:54

131

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Show that $\sum_{n\leq x}\frac{f(n)}{\sqrt n}=2L(1,\chi)\sqrt{x}+O(1)$, where $f(n)=\sum_{d\vert n}\chi(n)$.

Published on 04 Apr 2026 - 17:32

score 93 · Answer 5 · 2026-04-03 08:27:23

93

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Proof explanation that the Riemann hypothesis implies $L(x) = O(x^{\frac12 + \varepsilon})$, where $L(x) = \sum_{n\leq x}\lambda(n)$

Published on 03 Apr 2026 - 8:27

score 110 · Answer 6 · 2026-03-26 06:05:35

110

Views

Is this inequality related to $|\log \zeta (s)|$ wrong?

Published on 26 Mar 2026 - 6:05

score 78 · Answer 7 · 2026-04-02 07:08:23

78

Views

Bound on geometric mean of gcd

Published on 02 Apr 2026 - 7:08

score 112 · Answer 8 · 2026-02-23 07:20:46

112

Views

Evaluate $L(1, \chi) = \sum_{n=1}^\infty \frac{\chi(n)}{n}$ for $\chi$ mod $3$

Published on 23 Feb 2026 - 7:20

score 60 · Answer 9 · 2026-02-23 07:21:33

60

Views

Evaluate $L(1, \chi) = \sum_{n=1}^\infty \frac{\chi_5(n)}{n},$ for $\chi$ mod $5$

Published on 23 Feb 2026 - 7:21

score 49 · Answer 10 · 2026-04-01 10:44:15

49

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is there a notion of natural density over sets of integer with special structure?

Published on 01 Apr 2026 - 10:44

score 102 · Answer 11 · 2023-10-21 21:35:21

102

Views

Why is the smallest factor of 1 considered to be $\infty$ in analytic number theory?

Published on 21 Oct 2023 - 21:35

score 110 · Answer 12 · 2026-04-02 08:19:38

110

Views

Are there any real analytic functions such that $\sum_{n=1}^{\infty} \frac{1}{f(n)} = \sum_{k=2}^{\infty} f(k) \left( \zeta(k) - 1 \right) $?

Published on 02 Apr 2026 - 8:19

score 69 · Answer 13 · 2023-10-23 11:00:27

69

Views

Is $\prod_{p\ge 3} \left(1+p\left(\frac{1}{(p-1)^2}-\frac{1}{p^2}\right)\right) \ge 2$ where the product runs over all odd primes?

Published on 23 Oct 2023 - 11:00

score 99 · Answer 14 · 2023-10-24 22:13:35

99

Views

How to show $\sum_{n=0}^{q-1} ne^{2\pi i\frac{p}{q} n^2 } = -\frac{q}{2} $ a connection between Quadratic Gauss Sums and Cesaro Summation

Published on 24 Oct 2023 - 22:13

score 140 · Answer 15 · 2026-03-28 20:14:18

140

Views

How fast does the coprime probability converge to $6/\pi^2$?

Published on 28 Mar 2026 - 20:14

List Question

There are infinitely many non-harshad Fibonacci numbers

$\chi(n)=\frac{\tau_k(\chi)}{\sqrt k}\sum_{m=1}^k \bar\chi(m)e^{-\frac{2\pi imn}{k}}$

Modular functions and modular forms

Show that $\sum_{n\leq x}\frac{f(n)}{\sqrt n}=2L(1,\chi)\sqrt{x}+O(1)$, where $f(n)=\sum_{d\vert n}\chi(n)$.

Proof explanation that the Riemann hypothesis implies $L(x) = O(x^{\frac12 + \varepsilon})$, where $L(x) = \sum_{n\leq x}\lambda(n)$

Is this inequality related to $|\log \zeta (s)|$ wrong?

Bound on geometric mean of gcd

Evaluate $L(1, \chi) = \sum_{n=1}^\infty \frac{\chi(n)}{n}$ for $\chi$ mod $3$

Evaluate $L(1, \chi) = \sum_{n=1}^\infty \frac{\chi_5(n)}{n},$ for $\chi$ mod $5$

is there a notion of natural density over sets of integer with special structure?

Why is the smallest factor of 1 considered to be $\infty$ in analytic number theory?

Are there any real analytic functions such that $\sum_{n=1}^{\infty} \frac{1}{f(n)} = \sum_{k=2}^{\infty} f(k) \left( \zeta(k) - 1 \right) $?

Is $\prod_{p\ge 3} \left(1+p\left(\frac{1}{(p-1)^2}-\frac{1}{p^2}\right)\right) \ge 2$ where the product runs over all odd primes?

How to show $\sum_{n=0}^{q-1} ne^{2\pi i\frac{p}{q} n^2 } = -\frac{q}{2} $ a connection between Quadratic Gauss Sums and Cesaro Summation

How fast does the coprime probability converge to $6/\pi^2$?

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