# Questions tagged [algebraic-number-theory]

Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces

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### Extension of Erdos-Selfridge Theorem

**10**

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### Is there an elementary proof that there are infinitely many primes that are *not* completely split in an abelian extension?

**4**

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### Does the Gauss sum attached to $\chi$ ever belong to $\mathbb{Q}(\chi)$?

**1**

**1**answer

### Bound on number of proper ideals of norm equal to n

**4**

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### Hodge-Tate weights of cohomological cuspidal automorphic representation

**4**

**1**answer

### Why do polynomials $x^n + 1 \bmod N$ close a shorter cycle when $n$ is even than when $n$ is odd?

**0**

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### Absolute convergence of the Fourier series of a smooth adelic function

**37**

**1**answer

### Class field theory - a “dead end”?

**4**

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### Computation of Hochschild homology

**4**

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### Confusion about topological Hochschild homology and $\mathbb{Z}_p$-topological Hochschild homology

**6**

**1**answer

### The Hilbert symbols of quaternion algebras over a totally real field

**9**

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### How small may the discriminant of an $S_d$-field be?

**5**

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### How did Gauss find the units of the cubic field $Q[n^{1/3}]$?

**0**

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### Fundamental System of Neighborhoods of the Identity in $G(\mathbb{A}_f)$

**4**

**1**answer