All Questions
Tagged with reference-request nt.number-theory
1,408 questions
2
votes
0
answers
687
views
Strong Bezout's Identity?
Let $\{ a_i \}_{i=1}^N $ be a set of elements of the ring of integers, $\mathbb{Z}_D$ and define $g = \text{gcd}(a_1, a_2,\ldots, a_N, D)$. Then Bezout's Identity states that there exists another set $...
- 133
4
votes
0
answers
369
views
Reducing factoring prime products to factoring integer products (in average-case)
My question is about the equivalence of the security of various candidate one-way functions that can be constructed based on the hardness of factoring. (This question has been asked also in the CS ...
- 41
2
votes
0
answers
243
views
Hurwitz integers and $F_4$
The Hurwitz integers are
$$
\mathcal H=
\{a+bi+cj+dk:a,b,c,d\in\mathbb Z\;\text{ or } \;a,b,c,d\in \tfrac12+\mathbb Z\}.
$$
I want to know if there is a formula, for $m\in\mathbb Z$, for the number ...
- 2,446
1
vote
0
answers
86
views
Classification of involutions of the lattice $H\oplus H(k)^{\oplus2}$ for $k=5,6$?
Let $H$ denote the hyperbolic lattice (rank 2 lattice generated by $e,f$ such that $e^2=f^2=e.f-2=0$). Let $k >0$ be an integer. Is it possible to classify involutions $\iota$ of the lattice
$$
L:=...
- 1,663
1
vote
0
answers
162
views
Construction of RM abelian variety from eigenform
Let $f$ be a normalized eigenform of weight $2$ level $N$. If the Fourier coefficients of $f$ generate a totally real field $F$, then we associate to $f$ a system of $\ell$-adic Galois representations ...
- 15.4k
4
votes
1
answer
229
views
Sum of products with bounded coefficients
The following lemma is not hard to prove.
Lemma : Let $c_1 \neq c_2 \neq \dots \neq c_r \in [n]$ and $k \in [n]$. If $m_1, m_2, \dots, m_r$ are integers (some of them might be negative) such that $...
- 281
2
votes
0
answers
214
views
structure of $T_\ell A$ for $A/\mathbf{F}_q$ an abelian variety
Can someone give me references for the structure of the $G_{\mathbf{F}_q}$-module $T_\ell A$, $A/\mathbf{F}_q$ an abelian variety?
- 417
3
votes
1
answer
181
views
Reference request - spectral radius formula for linear transformations in char p
I am finishing up a paper and I would like to be able to quote a theorem that does what
is said in the title. To be specific let me introduce some notations:
${\bf F}$ is a local field of ...
