All Questions
Tagged with qa.quantum-algebra nt.number-theory
9 questions
12
votes
0
answers
552
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On a revised quantum Riemann hypothesis
This post provides a revision of the disproved quantum Riemann hypothesis proposed 2 years ago in this post, where you can refer to have more details about the motivations, the notations and the ...
34
votes
1
answer
3k
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On a quantum Riemann Hypothesis
Here is a revised version: On a revised quantum Riemann
hypothesis.
Robin's theorem (1984) states that
$$ \sigma(n) < e^\gamma n \log \log n$$
for all $n > 5040$ if and only if the Riemann ...
15
votes
1
answer
371
views
How are MTCs permuted by the Galois action on the little disk operad?
There is a well-studied action of $\operatorname{Gal}(\bar{\mathbb Q}/\mathbb Q)$ on (some version of) the $E_2$ operad; see for example this MO question.
Modular tensor categories are examples of $...
- 54.6k
7
votes
1
answer
417
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Bounding $p$-adic characters and Jacquet-Langlands transfert
I would like to bound uniformly in $\pi$ the $p$-adic Harisch-Chandra characters $\Theta_\pi$ for division quaternion algebras. By the Jacquet-Langlands correspondence, it is sufficient to bound it on ...
- 5,424
21
votes
1
answer
2k
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Gauss linking integral and quadratic reciprocity
In the setting of Mazur's "primes and knots" analogy, prime ideals $\mathfrak p\subset\mathcal O_K$ correspond to "knots" $\operatorname{Spec}\mathcal O_K/\mathfrak p$ inside a "3-manifold" $\...
- 18.7k
11
votes
3
answers
1k
views
A problem on a specific integer partition
Let $n$ be a positive integer, we consider partitions of the following form :
$$n = d^{2}_{1} + d^{2}_{2} + ... + d^{2}_{r}$$ such that :
$d_{i}\vert n$
$1=d_{1}<d_{2} \le d_{3} \le ... \le d_{r}$...
2
votes
1
answer
434
views
Divisibility Rules for Quantum Integers
I take a random but practical example direct from "R-matrices and the magic square"
by Bruce Westbury: The adjoint irrep $A$ of the $E_7$ family has quantum dimension
$qi[2*m+3]*qi[3*m/2+2]*qi[3*m/2]/...
- 4,829
2
votes
1
answer
309
views
A diophantine equation for the E8 knot polynomial family
Let $x,y,z$ be dimensions that appear in the Clebsch-Gordan series
$x*x=1+t+u+y+z$.
(E8 family if $t=x$ (say), but there is at least another family. E.g. B4(R4) belongs to the latter.)
With ...
- 4,829
4
votes
0
answers
246
views
Algorithm/denominators of elements of a rational affine space
I hope it's not a trivial question... Suppose I have a finite dimensional vector space $V$ over $\mathbb{Q}$ with a distinguished basis (in my case it's the $k$th graded piece of the free associative ...
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