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Results tagged with nt.number-theory
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user 108143
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
-1
votes
1
answer
308
views
Inert primes in arithmetic progression
Let $a,m$ an integers s.t $(a,m)=1$. Let $K$ a quadratic field, I would like to calculate the natural density of the set
$$\{p \;\; \text{rational prime}\; /\; p\;\text{inert in}\; K,\; p\equiv a\pmo …
- 111
5
votes
1
answer
275
views
Question about Fourier coefficients of a newform at primes
For $q:=e^{2\pi i z},$ let $f(z)=\sum_{n\ge 1}\lambda(n)n^{(k-1)/2}q^n$ be a normalized newform of type $(k,\chi)$ and level $N$. For any prime $p,$ we have
$$\lambda(p)=2\cos(\theta_p)\;\;\;\text{f …
- 111
4
votes
1
answer
243
views
Is there an $n\ge1$ such that every prime $p\equiv1\pmod{9}$ is representable in the form $x... [closed]
Is there an integer $n\ge1$ such that every prime $p\equiv1\pmod{9}$ is representable in the form $x^2+ny^2$?
- 111