Newest Questions
165,789 questions
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Are there known Lucas pseudoprimes defined by the simultaneous congruences U_{n+1} ≡ 0 (mod n) and U_{n-1} ≡ 1 (mod n)?
Consider the Lucas sequence (U_n) defined by
U_0 = 0,
U_1 = 1,
U_{n+1} = 5 U_n + 5 U_{n-1},
i.e. parameters (P,Q) = (5, -5) with discriminant D = 45.
For odd integers n with gcd(n,10) = 1, I consider ...
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0
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9
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Obstruction to multiplicative gluing of maximal-order elements in norm-1 tori arising from Lucas sequences
Question
Let (U_n) be the Lucas sequence defined by
U_0 = 0,
U_1 = 1,
U_{n+1} = 5 U_n + 5 U_{n-1},
with discriminant D = 45.
For an odd prime p congruent to 3 or 7 modulo 10, one has (D | p) = -1, so ...
3
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37
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Topological property of $B_{\mathrm{dR}}$ via exercise in Brinon-Conrad's $p$-adic Hodge theory notes
I'm currently working through Exercise 4.5.3 in Brinon-Conrad's $p$-adic Hodge theory notes and have been stuck on part 5 for a while now. In this exercise, we are examining the topology on $A_{\...
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20
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Does Hasse-Arf theorem help for infinite abelian extension of local field?
Let $K$ be a local field and let
$$K \subset L_1 \subset L_2 \subset \cdots$$
be a tower of finite abelian extensions and $L_{\infty}=\bigcup_nL_n$. Then $L_{\infty}/K$ is also abelian.
Let $G=\...
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0
answers
32
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Carmichael Lucas Number via the numbers of digits of Powers of two [closed]
The Number of digits of $2^{75893}$ Is 22847, a Lucas Carmichael Number.
Are there infinetily many n such that the Number of digits of $2^n$ Is a Lucas Carmichael?
Is the vias bias?
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How might one prove eventual descent for a divisor–sum/halving recursion implying the nonexistence of odd perfect numbers? [closed]
Let $n\ge 1$ and define a recursive sequence
$$
\mathcal R^0(n)=n,\qquad
\mathcal R^{k+1}(n)=
\begin{cases}
\sigma(\mathcal R^k(n)), & \text{if } \mathcal R^k(n)\text{ is odd},\\
\mathcal R^k(n)/2,...
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Toroidal Elton–Odell and the “rephasing trap” in the Ramsey reduction
Let $X$ be an infinite-dimensional complex Banach space and write
$$
d_{\mathbb T}(x,y):=\inf_{|\theta|=1}|x-\theta y|,\qquad x,y\in S_X.
$$
It is still open whether the “toroidal” Elton–Odell holds ...
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30
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Spectrum of a self-adjoint operator of rotation algebra $A_\theta,\;\theta=\frac{p}{q}$
I am reading the proof of 3.3 Theorem of "Gauss polynomials and the rotation algebra" and I have a question about the spectrum of a self-adjoint operator of a rotation algebra.
To begin with,...
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Is there any known model for π ( x ) that exceeds this level of precision? [closed]
While exploring the distribution of primes using Ordinal Probability Column Tables, I developed a structural dual-anchor methodology that seems to reach a very high level of deterministic precision. ...
2
votes
1
answer
53
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Sum of the two decomposable measures
Definition. Let $(X, \mathscr{A}, \mu)$ be a measure space. Suppose that there is a subfamily $\mathscr{F}$ of $\mathscr{A}$ with the following properties:
(i) $0 \leqq \mu(F) < \infty$ for all $F \...
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votes
1
answer
46
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Subdegrees of affine primitive permutation groups
Let $G\leq {\rm AGL}(d,p)$ be an affine primitive permutation group of degree $p^d$. Is it true that any subdegree of $G$ is coprime to $p$?
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Equivariant embeddings of manifolds into representations
For a given compact Lie (or even finite or even $C_p$) group $G$ and a $G$-equivariant compact smooth manifold $M$, one can find a smooth embedding of $M$ into a representation of $G$. I have ...
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115
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Elements of $\pi_2$ can be approximated by smooth embeddings
Suppose $M$ is a compact $4$-dimensional manifold with empty boundary (so $M$ is closed) and $\pi_1(M)$ is not trivial (i.e., $M$ is not simply connected). Suppose $\alpha\colon S^2\to M$ corresponds ...
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Embeddability order on Picard groups
Consider a commutative ring $R$ and its Picard group $\mathrm{Pic}(R)$. For two invertible $R$-modules $M,N$, we may define $[M]\le [N]$ to mean that there exists an injective $R$-linear map from $M$ ...
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votes
1
answer
89
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Explicit bases for orthogonal group irreps
Let $n\in \mathbb{N}$ and $a \leq n$. Let $\mathbb{C}^{2n}$ denote the standard representation of $GL(2n)$ with basis $\{e_{1},\ldots, e_{2n}\}$.
Consider the irrep decomposition of $GL(2n)$ ...
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