# Questions tagged [nt.number-theory]

Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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### Infinite tamely ramified $p$-extensions of $\mathbb{Q}$ contain infinite unramified subextensions?

Let $p$ be a prime. By a $p$-extension we mean a Galois extension whose Galois group is a $p$-group. Let $L$ be an infinite tamely ramified $p$-extension of $\mathbb{Q}$, i.e. all primes ramified ...
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### Fourier series of Eisenstein series — elegant and very good approximation

I played around with the Fourier series of the Eisenstein series resp. divisor sums and did some calculations, see below. Although the deduction is not rigorous / wrong (as the power series for the ...
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### Existence of fully supported element in a finite-dimensional vector space over $\mathbb{F}_p$ (and in finite abelian groups)

Let $V$ be an $n$-dimensional vector space over $\mathbb{F} = \mathbb{Z} / (p)$, the field of $p$ elements, $p$ a prime, with $\{v_1, \dotsc, v_n \}$ a basis for $V$. An element $x \in V$ is called &...
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### Langlands-Shahidi method in classical language

The Langlands-Shahidi method says that the $L$-functions of automorphic representations appear in the constant terms of Eisenstein series. Since those Eisenstein series have analytic continuation and ...
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