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Results tagged with nt.number-theory
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user 22989
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
5
votes
A question on bi-character of finite abelian group
You can choose integers $m_1,m_2,n_1,n_2$ so that $m_1$ and $n_1$ are coprime to $p$ and $m_2$ and $n_2$ are coprime to $q$, and such that $n_1m_2b(a_1,b_2)=0=n_2m_1b(a_2,b_1)$.
Then
$$b(n_1a_1+n_2a_2 …
- 35.2k
13
votes
Accepted
Can we glue characteristic 0 and characteristic p representations of a finite group given eq...
The condition on Brauer characters is not sufficient.
Let $G$ be a $p$-group, $\pi$ any nontrivial representation over $\mathbb{F}_p$, and $\sigma$ the trivial representation over $\mathbb{Q}_p$ of t …
- 35.2k
5
votes
Accepted
Periods in the trivial extension algebra of the incidence algebra of the divisor lattice
Calculating periods of simple modules for the trivial extension algebra $TA$ can be reduced to a calculation with $A$-modules (at least if $A$ has finite global dimension), which is much easier.
The …
- 35.2k
6
votes
Accepted
Number of homomorphism, or number of solution to equations, in finite groups
There are $70$ homomorphisms from $\mathbb{Z}\times\mathbb{Z}$ to the dihedral group of order $14$.
- 35.2k
13
votes
Bass' stable range of $\mathbf Z[X]$
There's a comment at the top of page 993 of
L N Vaseršteĭn, A A Suslin, "Serre's problem on projective modules over polynomial rings, and algebraic K-theory", Math. USSR Izv., 1976, 10 (5), 937–1001, …
- 35.2k